Publications

1. Ling-Bing He, Jie Ji and Wei-Xi Li.
   On the Boltzmann equation with soft potentials: Existence, uniqueness and smoothing effect of mild solutions.
   Preprint. arXiv:2410.13205
   
   arXiv   
2. Wei-Xi Li, Zhan Xu and Anita Yang
   Global well-posedness of the MHD boundary layer equations in the Sobolev Space
   Sci. China Math.(Accepted).
   arXiv   
3. Wei-Xi Li, Xiaojing Xu and Tianyuan Yu
   On the hydrostatic approximation of the 3D Boussinesq equations of damped wave type
   SIAM J. Math. Anal. 57 (2025), no. 3, 2952–2982
   
   DOI    Bibtex

   @article {MR4915128,
       AUTHOR = {Li, Wei-Xi and Xu, Xiaojing and Yu, Tianyuan},
        TITLE = {On the {H}ydrostatic {A}pproximation of the 3{D} {B}oussinesq
                 {E}quations of {D}amped {W}ave {T}ype},
      JOURNAL = {SIAM J. Math. Anal.},
     FJOURNAL = {SIAM Journal on Mathematical Analysis},
       VOLUME = {57},
         YEAR = {2025},
       NUMBER = {3},
        PAGES = {2952--2982},
         ISSN = {0036-1410},
      MRCLASS = {35Q35 (76D03 76D10)},
     MRNUMBER = {4915128},
          DOI = {10.1137/24M1661303},
          URL = {https://doi.org/10.1137/24M1661303},
   }
   

4. Jun-Ling Chen, Wei-Xi Li and Chao-Jiang Xu
   Sharp regularization effect for the non-cutoff Boltzmann equation with hard potentials
   Ann. Inst. H. Poincaré C Anal. Non Linéaire 42 (2025), no. 4, 933–970.
   arXiv    DOI    Bibtex

    
   @article {MR4930523,
       AUTHOR = {Chen, Jun-Ling and Li, Wei-Xi and Xu, Chao-Jiang},
        TITLE = {Sharp regularization effect for the non-cutoff {B}oltzmann
                 equation with hard potentials},
      JOURNAL = {Ann. Inst. H. Poincar\'{e} C Anal. Non Lin\'{e}aire},
     FJOURNAL = {Annales de l'Institut Henri Poincar\'{e} C. Analyse Non Lin\'{e}aire},
       VOLUME = {42},
         YEAR = {2025},
       NUMBER = {4},
        PAGES = {933--970},
         ISSN = {0294-1449},
      MRCLASS = {35B65 (35Q20)},
     MRNUMBER = {4930523},
          DOI = {10.4171/aihpc/121},
          URL = {https://doi.org/10.4171/aihpc/121},
   }
   
   

5. Ke Chen, Wei-Xi Li and Tong Yang.
   Local Well-Posedness of the Three Dimensional Linearized MHD Boundary Layer System.
   Communications in Mathematical Analysis and Applications 3(2024), No. 4, 483-500
   DOI    Bibtex

    
   @article {MR4834601,
       AUTHOR = {Chen, Ke and Li, Wei-Xi and Yang, Tong},
        TITLE = {Local well-posedness of the three dimensional linearized {MHD}
                 boundary layer system},
      JOURNAL = {Commun. Math. Anal. Appl.},
     FJOURNAL = {Communications in Mathematical Analysis and Applications},
       VOLUME = {3},
         YEAR = {2024},
       NUMBER = {4},
        PAGES = {483--500},
         ISSN = {2790-1920},
      MRCLASS = {76D10 (35G31 35Q35 76W05)},
     MRNUMBER = {4834601},
   }
   
   

6. Wei-Xi Li, Marius Paicu and Ping Zhang
   Gevrey solutions of quasi-linear hyperbolic hydrostatic Navier-Stokes system
   SIAM Journal on Mathematical Analysis 55 (2023), no. 6, 6194–6228
   
   DOI    Bibtex

   @article {MR4661716,
       AUTHOR = {Li, Wei-Xi and Paicu, Marius and Zhang, Ping},
        TITLE = {Gevrey solutions of quasi-linear hyperbolic hydrostatic
                 {N}avier-{S}tokes system},
      JOURNAL = {SIAM J. Math. Anal.},
     FJOURNAL = {SIAM Journal on Mathematical Analysis},
       VOLUME = {55},
         YEAR = {2023},
       NUMBER = {6},
        PAGES = {6194--6228},
         ISSN = {0036-1410},
      MRCLASS = {35Q30 (35L72 76D03)},
     MRNUMBER = {4661716},
          DOI = {10.1137/22M1526290},
          URL = {https://doi.org/10.1137/22M1526290},
   }
   

7. Wei-Xi Li, Tong Yang and Ping Zhang
   Gevrey well-posedness of quasi-linear hyperbolic Prandtl equations
   Communications in Mathematical Analysis and Applications 2 (2023), no. 4, 388–420
   DOI    Bibtex

   @article {MR4726840,
       AUTHOR = {Li, Wei-Xi and Yang, Tong and Zhang, Ping},
        TITLE = {Gevrey well-posedness of quasi-linear hyperbolic {P}randtl
                 equations},
      JOURNAL = {Commun. Math. Anal. Appl.},
     FJOURNAL = {Communications in Mathematical Analysis and Applications},
       VOLUME = {2},
         YEAR = {2023},
       NUMBER = {4},
        PAGES = {388--420},
         ISSN = {2790-1920},
      MRCLASS = {76D10 (35L72 35L80 35Q30 76D03)},
     MRNUMBER = {4726840},
   }
   

8. Hongmei Cao, Wei-Xi Li and Chao-Jiang Xu
   Analytic smoothing effect of the spatially inhomogeneous Landau equations for hard potentials.
   Journal de Mathématiques Pures et Appliquées 176 (2023), 138–182.
   arXiv    DOI    Bibtex

   @article {MR4612704,
       AUTHOR = {Cao, Hongmei and Li, Wei-Xi and Xu, Chao-Jiang},
        TITLE = {Analytic smoothing effect of the spatially inhomogeneous
                 {L}andau equations for hard potentials},
      JOURNAL = {J. Math. Pures Appl. (9)},
     FJOURNAL = {Journal de Math\'{e}matiques Pures et Appliqu\'{e}es.
                 Neuvi\`eme S\'{e}rie},
       VOLUME = {176},
         YEAR = {2023},
        PAGES = {138--182},
         ISSN = {0021-7824,1776-3371},
      MRCLASS = {35B65 (35H20 35Q20 35Q82)},
     MRNUMBER = {4612704},
          DOI = {10.1016/j.matpur.2023.06.004},
          URL = {https://doi.org/10.1016/j.matpur.2023.06.004},
   }
   

9. Wei-Xi Li, Rui Xu and Tong Yang
   Global Well-posedness of a Prandtl Model from MHD in Gevrey Function Spaces.
   Acta Mathematica Scientia, 42(2022), no. 6, 2343-2366. Dedicated to Professor Banghe LI on the occasion of his 80th birthday
   arXiv    DOI    Bibtex

   @article {MR4494626,
       AUTHOR = {Li, Wei-Xi and Xu, Rui and Yang, Tong},
        TITLE = {Global well-posedness of a {P}randtl model from {MHD} in
                 {G}evrey function spaces},
      JOURNAL = {Acta Math. Sci. Ser. B (Engl. Ed.)},
     FJOURNAL = {Acta Mathematica Scientia. Series B. English Edition},
       VOLUME = {42},
         YEAR = {2022},
       NUMBER = {6},
        PAGES = {2343--2366},
         ISSN = {0252-9602},
      MRCLASS = {76W05 (35M33 35Q35)},
     MRNUMBER = {4494626},
          DOI = {10.1007/s10473-022-0609-7},
          URL = {https://doi.org/10.1007/s10473-022-0609-7},
   }
   

10. Wei-Xi Li and Tong Yang,
    3D hyperbolic Navier-Stokes equations in a thin strip: global well-posedness and hydrostatic limit in Gevrey space.
    Communications in Mathematical Analysis and Applications, 1 (2022), 471-502.
    arXiv    DOI    Bibtex

    @article {MR4700999,
        AUTHOR = {Li, Wei-Xi and Yang, Tong},
         TITLE = {3{D} hyperbolic {N}avier-{S}tokes equations in a thin strip:
                  global well-posedness and hydrostatic limit in {G}evrey space},
       JOURNAL = {Commun. Math. Anal. Appl.},
      FJOURNAL = {Communications in Mathematical Analysis and Applications},
        VOLUME = {1},
          YEAR = {2022},
        NUMBER = {4},
         PAGES = {471--502},
          ISSN = {2790-1920},
       MRCLASS = {76D03 (35Q30 76D05)},
      MRNUMBER = {4700999},
    }
    
    

11. Wei-Xi Li and Rui Xu,
    Gevrey well-posedness of the hyperbolic Prandtl equations.
    Communications in Mathematical Research, 38 (2022), no. 4, 605–624. In honor of Professor Chao-Jiang Xu on the occasion of his 65th birthday
    arXiv    DOI    Bibtex

    @article {MR4498949,
        AUTHOR = {Li, Wei-Xi and Xu, Rui},
         TITLE = {Gevrey well-posedness of the hyperbolic {P}randtl equations},
       JOURNAL = {Commun. Math. Res.},
      FJOURNAL = {Communications in Mathematical Research},
        VOLUME = {38},
          YEAR = {2022},
        NUMBER = {4},
         PAGES = {605--624},
          ISSN = {1674-5647},
       MRCLASS = {35Q35 (76D10)},
      MRNUMBER = {4498949},
    MRREVIEWER = {Suhua Lai},
    }
    

12. Wei-Xi Li, Nader Masmoudi and Tong Yang.
    Well-posedness in Gevrey function space for 3D Prandtl equations without Structural Assumption.
    Communications on Pure and Applied Mathematics 75(2022), 1755–1797.
    

    @article {MR4465902,
        AUTHOR = {Li, Wei-Xi and Masmoudi, Nader and Yang, Tong},
         TITLE = {Well-posedness in {G}evrey function space for 3{D} {P}randtl
                  equations without structural assumption},
       JOURNAL = {Comm. Pure Appl. Math.},
      FJOURNAL = {Communications on Pure and Applied Mathematics},
        VOLUME = {75},
          YEAR = {2022},
        NUMBER = {8},
         PAGES = {1755--1797},
          ISSN = {0010-3640},
       MRCLASS = {76D10},
      MRNUMBER = {4465902},
           DOI = {10.1002/cpa.21989},
           URL = {https://doi.org/10.1002/cpa.21989},
    }

    arxiv • DOI • Bibtex
13. Renjun Duan, Wei-Xi Li and Lvqiao Liu,
    Gevrey regularity of a mild solution to the non-cutoff Boltzmann equation.
    Advances in Mathematics 395 (2022), Paper No. 108159, 75pp.

    @article {MR4356815,
        AUTHOR = {Duan, Renjun and Li, Wei-Xi and Liu, Lvqiao},
         TITLE = {Gevrey regularity of mild solutions to the non-cutoff
                  {B}oltzmann equation},
       JOURNAL = {Adv. Math.},
      FJOURNAL = {Advances in Mathematics},
        VOLUME = {395},
          YEAR = {2022},
         PAGES = {Paper No. 108159},
          ISSN = {0001-8708},
       MRCLASS = {35Q20 (35B20 35B65 35H10)},
      MRNUMBER = {4356815},
           DOI = {10.1016/j.aim.2021.108159},
           URL = {https://doi.org/10.1016/j.aim.2021.108159},
    }
    

    arXiv • DOI • Bibtex
14. Hua Chen, Xin Hu, Wei-Xi Li and Jinpeng Zhan,
    The Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off.
    Science China Mathematics 65 (2022), no. 3, 443–470

    @article {MR4375857,
        AUTHOR = {Chen, Hua and Hu, Xin and Li, Wei-Xi and Zhan, Jinpeng},
         TITLE = {The {G}evrey smoothing effect for the spatially inhomogeneous
                  {B}oltzmann equations without cut-off},
       JOURNAL = {Sci. China Math.},
      FJOURNAL = {Science China. Mathematics},
        VOLUME = {65},
          YEAR = {2022},
        NUMBER = {3},
         PAGES = {443--470},
          ISSN = {1674-7283},
       MRCLASS = {35B65 (35H10 35Q20)},
      MRNUMBER = {4375857},
           DOI = {10.1007/s11425-021-1886-9},
           URL = {https://doi.org/10.1007/s11425-021-1886-9},
    }
    

    arXiv • DOI • Bibtex
15. Wei-Xi Li and Rui Xu.
    Well-posedness in Sobolev spaces of the two-dimensional MHD Boundary layer equations without viscosity.
    Electronic Research Archive 29 (2021), no. 6, 4243-4255

    @article {MR4342301,
        AUTHOR = {Li, Wei-Xi and Xu, Rui},
         TITLE = {Well-posedness in {S}obolev spaces of the two-dimensional
                  {MHD} boundary layer equations without viscosity},
       JOURNAL = {Electron. Res. Arch.},
      FJOURNAL = {Electronic Research Archive},
        VOLUME = {29},
          YEAR = {2021},
        NUMBER = {6},
         PAGES = {4243--4255},
       MRCLASS = {35Q35 (76D10 76W05)},
      MRNUMBER = {4342301},
           DOI = {10.3934/era.2021082},
           URL = {https://doi.org/10.3934/era.2021082},
    }

    arXiv • DOI • Bibtex
16. Wei-Xi Li and Chao-Jiang Xu.
    Subellipticity of some complex vector fields related to Witten Laplacian.
    Communications on Pure and Applied Analysis 20 (2021), no. 7-8, 2709-2724. Special issue in Honor of the 80th birthday of Professor Shuxing Chen.

    @article {MR4312130,
        AUTHOR = {Li, Wei Xi and Xu, Chao Jiang},
         TITLE = {Subellipticity of some complex vector fields related to the
                  {W}itten {L}aplacian},
       JOURNAL = {Commun. Pure Appl. Anal.},
      FJOURNAL = {Communications on Pure and Applied Analysis},
        VOLUME = {20},
          YEAR = {2021},
        NUMBER = {7-8},
         PAGES = {2709--2724},
          ISSN = {1534-0392},
       MRCLASS = {35H20 (35H10)},
      MRNUMBER = {4312130},
           DOI = {10.3934/cpaa.2021047},
           URL = {https://doi.org/10.3934/cpaa.2021047},
    }
    

    arXiv • DOI • Bibtex
17. Wei-Xi Li and Tong Yang,
    Well-posedness of the MHD boundary layer system in Gevrey function space without Structural Assumption.
    SIAM Journal on Mathematical Analysis 53 (2021), No.3, 3236-3264

    @article {MR4270479,
        AUTHOR = {Li, Wei-Xi and Yang, Tong},
         TITLE = {Well-posedness of the {MHD} {B}oundary {L}ayer {S}ystem in
                  {G}evrey {F}unction {S}pace without {S}tructural {A}ssumption},
       JOURNAL = {SIAM J. Math. Anal.},
      FJOURNAL = {SIAM Journal on Mathematical Analysis},
        VOLUME = {53},
          YEAR = {2021},
        NUMBER = {3},
         PAGES = {3236--3264},
          ISSN = {0036-1410},
       MRCLASS = {35Q35 (76W05)},
      MRNUMBER = {4270479},
           DOI = {10.1137/20M1367027},
           URL = {http://doi.org/10.1137/20M1367027},
    }
    

    arXiv • DOI • Bibtex
18. Wei-Xi Li and Juan Zeng.
    Weighted and maximally hypoelliptic estimates for the Fokker-Planck Operator with electromagnetic fields.
    Communications in Mathematical Research 37 (2021), pp. 255-270.

    @article {MR4238433,
        AUTHOR = {Li, Wei-Xi and Zeng, Juan},
         TITLE = {Weighted and maximally hypoelliptic estimates for the
                  {F}okker-{P}lanck operator with electromagnetic fields},
       JOURNAL = {Commun. Math. Res.},
      FJOURNAL = {Communications in Mathematical Research},
        VOLUME = {37},
          YEAR = {2021},
        NUMBER = {2},
         PAGES = {255--270},
          ISSN = {1674-5647},
       MRCLASS = {35H20 (35Q84 78A25)},
      MRNUMBER = {4238433},
           DOI = {10.4208/cmr.2020-0055},
           URL = {http://doi.org/10.4208/cmr.2020-0055},
    }

    arXiv • DOI • Bibtex
19. Wei-Xi Li and Lvqiao Liu.
    Gelfand-Shilov smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off.
    Kinetic and Related Models 13(2020), no. 5, 1029-1046

    @article {MR4147430,
        AUTHOR = {Li, Wei-Xi and Liu, Lvqiao},
         TITLE = {Gelfand-{S}hilov smoothing effect for the spatially
                  inhomogeneous {B}oltzmann equations without cut-off},
       JOURNAL = {Kinet. Relat. Models},
      FJOURNAL = {Kinetic and Related Models},
        VOLUME = {13},
          YEAR = {2020},
        NUMBER = {5},
         PAGES = {1029--1046},
          ISSN = {1937-5093},
       MRCLASS = {35Q20 (35B65 35H10)},
      MRNUMBER = {4147430},
           DOI = {10.3934/krm.2020036},
           URL = {http://doi.org/10.3934/krm.2020036},
    }  

    arXiv • DOI • Bibtex
20. Hua Chen, Xin Hu, Wei-Xi Li and Jinpeng Zhan.
    The resolvent of the linearized Boltzmann operator with a stationary potential.
    Journal of Pseudo-Differential Operators and Applications 11 (2020), no. 2, 733–751

     @article {MR4098118,
        AUTHOR = {Chen, Hua and Hu, Xin and Li, Wei-Xi and Zhan, Jinpeng},
         TITLE = {The resolvent of the linearized {B}oltzmann operator with a
                  stationary potential},
       JOURNAL = {J. Pseudo-Differ. Oper. Appl.},
      FJOURNAL = {Journal of Pseudo-Differential Operators and Applications},
        VOLUME = {11},
          YEAR = {2020},
        NUMBER = {2},
         PAGES = {733--751},
          ISSN = {1662-9981},
       MRCLASS = {35Q20 (47A10)},
      MRNUMBER = {4098118},
           DOI = {10.1007/s11868-019-00305-2},
           URL = {http://doi.org/10.1007/s11868-019-00305-2},
    } 

    DOI • Bibtex
21. Wei-Xi Li and Tong Yang.
    Well-posedness in Gevrey function space for the Prandtl equations with non-degenerate critical points.
    Journal of the European Mathematical Society , 22(2020) 717-775
    

    @article {MR4055987,
        AUTHOR = {Li, Wei-Xi and Yang, Tong},
         TITLE = {Well-posedness in {G}evrey function spaces for the {P}randtl
                  equations with non-degenerate critical points},
       JOURNAL = {J. Eur. Math. Soc. (JEMS)},
      FJOURNAL = {Journal of the European Mathematical Society (JEMS)},
        VOLUME = {22},
          YEAR = {2020},
        NUMBER = {3},
         PAGES = {717--775},
          ISSN = {1435-9855},
       MRCLASS = {35Q35 (35B30 35L60 35Q31)},
      MRNUMBER = {4055987},
           DOI = {10.4171/jems/931},
           URL = {http://doi.org/10.4171/jems/931},
    }

    PDF • DOI • Bibtex
22. Wei-Xi Li, Van-Sang Ngo and Chao-Jiang Xu.
    Boundary layer analysis for the fast horizontal rotating fluids.
    Communications in Mathematical Sciences 17(2019), 299-338
    

     @article {MR3983729,
        AUTHOR = {Li, Wei-Xi and Ngo, Van-Sang and Xu, Chao-Jiang},
         TITLE = {Boundary layer analysis for the fast horizontal rotating
                  fluids},
       JOURNAL = {Commun. Math. Sci.},
      FJOURNAL = {Communications in Mathematical Sciences},
        VOLUME = {17},
          YEAR = {2019},
        NUMBER = {2},
         PAGES = {299--338},
          ISSN = {1539-6746},
       MRCLASS = {35Q30 (35B25 35Q35 76U05)},
      MRNUMBER = {3983729},
           DOI = {10.4310/CMS.2019.v17.n2.a1},
           URL = {http://doi.org/10.4310/CMS.2019.v17.n2.a1},
    } 

    arXiv • DOI • Bibtex
23. Radjesvarane Alexandre, Frédéric Hérau and Wei-Xi Li.
    Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff.
    Journal de Mathématiques Pures et Appliquées 126(2019), 1–71

     @article {MR3950012,
        AUTHOR = {Alexandre, Radjesvarane and H\'{e}rau, Fr\'{e}d\'{e}ric and Li, Wei-Xi},
         TITLE = {Global hypoelliptic and symbolic estimates for the linearized
                  {B}oltzmann operator without angular cutoff},
       JOURNAL = {J. Math. Pures Appl. (9)},
      FJOURNAL = {Journal de Math\'{e}matiques Pures et Appliqu\'{e}es. Neuvi\`eme S\'{e}rie},
        VOLUME = {126},
          YEAR = {2019},
         PAGES = {1--71},
          ISSN = {0021-7824},
       MRCLASS = {35Sxx (35B65 35H10 35H20 35Q20 82C40)},
      MRNUMBER = {3950012},
    MRREVIEWER = {Luigi Rodino},
           DOI = {10.1016/j.matpur.2019.04.013},
           URL = {http://doi.org/10.1016/j.matpur.2019.04.013},
    }

    arXiv • DOI • Bibtex
24. Wei-Xi Li.
    Spectral Analysis for Fokker-Planck operator and Witten Laplacian (in Chinese)
    SCIENTIA SINICA Mathematica 49(2019),161-174. In Honor of the 90th birthday of Professor Minyou Qi.
    

    – In this survey paper we will review the classical hypoelliptic techniques and their global counterparts developed recently for the spectral analysis of the operators in mathematical physics. In particular we will focus on the compactness criteria for Fokker-Planck operator and Witten Laplacian and the close relationship between the two operators.

    PDF • DOI
25. Wei-Xi Li, Alberto Parmeggiani and Yan-Lin Wang.
    Global Gevrey hypoellipticity for the twisted Laplacian on forms.
    Journal of Pseudo-Differential Operators and Applications 9(2018), 151–171

    @article {MR3804032,
        AUTHOR = {Li, Wei-Xi and Parmeggiani, Alberto and Wang, Yan-Lin},
         TITLE = {Global {G}evrey hypoellipticity for the twisted {L}aplacian on
                  forms},
       JOURNAL = {J. Pseudo-Differ. Oper. Appl.},
      FJOURNAL = {Journal of Pseudo-Differential Operators and Applications},
        VOLUME = {9},
          YEAR = {2018},
        NUMBER = {2},
         PAGES = {151--171},
          ISSN = {1662-9981},
       MRCLASS = {35H10 (35B65)},
      MRNUMBER = {3804032},
    MRREVIEWER = {Qi Han},
           DOI = {10.1007/s11868-017-0232-x},
           URL = {http://doi.org/10.1007/s11868-017-0232-x},
    }

    PDF • DOI • Bibtex
26. Wei-Xi Li.
    Compactness criteria for the resolvent of the Fokker-Planck operator.
    Annali della Scuola Normale Superiore di Pisa, Classe di Scienze , Vol. 18, issue 1 (2018), 119-143

    @article {MR3783786,
        AUTHOR = {Li, Wei-Xi},
         TITLE = {Compactness criteria for the resolvent of the
                  {F}okker-{P}lanck operator},
       JOURNAL = {Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)},
      FJOURNAL = {Annali della Scuola Normale Superiore di Pisa. Classe di
                  Scienze. Serie V},
        VOLUME = {18},
          YEAR = {2018},
        NUMBER = {1},
         PAGES = {119--143},
          ISSN = {0391-173X},
       MRCLASS = {35Q84 (35H10 35P05 47A10)},
      MRNUMBER = {3783786},
    }

    PDF • DOI • Bibtex
27. Wei-Xi Li.
    Compactness of the resolvent for the Witten Laplacian.
    Annales Henri Poincaré 19 (2018), 1259-1282
    

    @article {MR3775156,
        AUTHOR = {Li, Wei-Xi},
         TITLE = {Compactness of the resolvent for the {W}itten {L}aplacian},
       JOURNAL = {Ann. Henri Poincar\'{e}},
      FJOURNAL = {Annales Henri Poincar\'{e}. A Journal of Theoretical and
                  Mathematical Physics},
        VOLUME = {19},
          YEAR = {2018},
        NUMBER = {4},
         PAGES = {1259--1282},
          ISSN = {1424-0637},
       MRCLASS = {35J10 (58J50 81Q05 81Q12)},
      MRNUMBER = {3775156},
    MRREVIEWER = {Leonid Friedlander},
           DOI = {10.1007/s00023-018-0659-5},
           URL = {http://doi.org/10.1007/s00023-018-0659-5},
    }

    PDF • DOI • Bibtex
28. Feng Cheng , Wei-Xi Li and Chao-Jiang Xu.
    Vanishing viscosity of Navier-Stokes flow to ideal flow in Gevrey space.
    Mathematical Methods in the Applied Sciences 40(2017), 5161–5176

    @article {MR3689256,
        AUTHOR = {Cheng, Feng and Li, Wei-Xi and Xu, Chao-Jiang},
         TITLE = {Vanishing viscosity limit of {N}avier-{S}tokes equations in
                  {G}evrey class},
       JOURNAL = {Math. Methods Appl. Sci.},
      FJOURNAL = {Mathematical Methods in the Applied Sciences},
        VOLUME = {40},
          YEAR = {2017},
        NUMBER = {14},
         PAGES = {5161--5176},
          ISSN = {0170-4214},
       MRCLASS = {35Q30 (35B25)},
      MRNUMBER = {3689256},
           DOI = {10.1002/mma.4378},
           URL = {http://doi.org/10.1002/mma.4378},
    }

    PDF • DOI • Bibtex
29. Feng Cheng , Wei-Xi Li and Chao-Jiang Xu.
    Gevery regularity with weight for incompressible Euler equation in the half plane.
    Acta Mathematics Scientia 37 (2017), no. 4, 1115-1132

    @article {MR3657211,
        AUTHOR = {Cheng, Feng and Li, Wei-Xi and Xu, Chao-Jiang},
         TITLE = {Gevrey regularity with weight for incompressible {E}uler
                  equation in the half plane},
       JOURNAL = {Acta Math. Sci. Ser. B (Engl. Ed.)},
      FJOURNAL = {Acta Mathematica Scientia. Series B. English Edition},
        VOLUME = {37},
          YEAR = {2017},
        NUMBER = {4},
         PAGES = {1115--1132},
          ISSN = {0252-9602},
       MRCLASS = {35M33 (35Q31 76B03)},
      MRNUMBER = {3657211},
           DOI = {10.1016/S0252-9602(17)30061-9},
           URL = {http://doi.org/10.1016/S0252-9602(17)30061-9},
    }

    PDF • DOI • Bibtex
30. Wei-Xi Li, Di Wu and Chao-Jiang Xu.
    Gevrey Class Smoothing Effect for the Prandtl Equation.
    SIAM Journal on Mathematical Analysis 48 (2016),1672–1726

    @article {MR3493958,
        AUTHOR = {Li, Wei-Xi and Wu, Di and Xu, Chao-Jiang},
         TITLE = {Gevrey class smoothing effect for the {P}randtl equation},
       JOURNAL = {SIAM J. Math. Anal.},
      FJOURNAL = {SIAM Journal on Mathematical Analysis},
        VOLUME = {48},
          YEAR = {2016},
        NUMBER = {3},
         PAGES = {1672--1726},
          ISSN = {0036-1410},
       MRCLASS = {35Q35 (35A20 35B65 76D03 76D09 76D10)},
      MRNUMBER = {3493958},
           DOI = {10.1137/15M1020368},
           URL = {http://doi.org/10.1137/15M1020368},
    }

    PDF • DOI • Bibtex
31. Wei-Xi Li, Peng Luo and Shuying Tian.
    $L^2$-regularity of kinetic equations with external potential.
    Journal of Differential Equations 260 (2016), 5894-5911

    @article {MR3456819,
        AUTHOR = {Li, Wei-Xi and Luo, Peng and Tian, Shuying},
         TITLE = {{$L^2$}-regularity of kinetic equations with external
                  potential},
       JOURNAL = {J. Differential Equations},
      FJOURNAL = {Journal of Differential Equations},
        VOLUME = {260},
          YEAR = {2016},
        NUMBER = {7},
         PAGES = {5894--5911},
          ISSN = {0022-0396},
       MRCLASS = {35H10 (35B65 35Q20 35Q84)},
      MRNUMBER = {3456819},
           DOI = {10.1016/j.jde.2015.12.022},
           URL = {http://doi.org/10.1016/j.jde.2015.12.022},
    }
    

    PDF • DOI • Bibtex
32. Wei-Xi Li.
    Global hypoelliptic estimates for fractional order kinetic equation.
    Mathematische Nachrichten 287(2014), 610-637

    @article {MR3193940,
        AUTHOR = {Li, Wei-Xi},
         TITLE = {Global hypoelliptic estimates for fractional order kinetic
                  equation},
       JOURNAL = {Math. Nachr.},
      FJOURNAL = {Mathematische Nachrichten},
        VOLUME = {287},
          YEAR = {2014},
        NUMBER = {5-6},
         PAGES = {610--637},
          ISSN = {0025-584X},
       MRCLASS = {35H10 (35Q20 35R11 82C40)},
      MRNUMBER = {3193940},
           DOI = {10.1002/mana.201200002},
           URL = {https://doi.org/10.1002/mana.201200002},
    }

    PDF • DOI • Bibtex
33. Hua Chen, Wei-Xi Li and Ling-Jun Wang.
    Regularity of traveling free surface water waves with vorticity.
    Journal of Nonlinear Science 23(2013), 1111-1142

    @article {MR3132078,
        AUTHOR = {Chen, Hua and Li, Wei-Xi and Wang, Ling-Jun},
         TITLE = {Regularity of traveling free surface water waves with
                  vorticity},
       JOURNAL = {J. Nonlinear Sci.},
      FJOURNAL = {Journal of Nonlinear Science},
        VOLUME = {23},
          YEAR = {2013},
        NUMBER = {6},
         PAGES = {1111--1142},
          ISSN = {0938-8974},
       MRCLASS = {35Q35 (35A20 35B65 35C07 76B15)},
      MRNUMBER = {3132078},
    MRREVIEWER = {Robert A. Van Gorder},
           DOI = {10.1007/s00332-013-9181-6},
           URL = {http://doi.org/10.1007/s00332-013-9181-6},
    }

    PDF • DOI • Bibtex
34. Frédéric Hérau and Wei-Xi Li.
    Global hypoelliptic estimates for Landau-type operator with external potential.
    Kyoto Journal of Mathematics 53 (2013), 533-565

    @article {MR3102561,
        AUTHOR = {H\'{e}rau, Fr\'{e}d\'{e}ric and Li, Wei-Xi},
         TITLE = {Global hypoelliptic estimates for {L}andau-type operators with
                  external potential},
       JOURNAL = {Kyoto J. Math.},
      FJOURNAL = {Kyoto Journal of Mathematics},
        VOLUME = {53},
          YEAR = {2013},
        NUMBER = {3},
         PAGES = {533--565},
          ISSN = {2156-2261},
       MRCLASS = {35H10 (35B65 35H20 35Q84 82C40)},
      MRNUMBER = {3102561},
    MRREVIEWER = {Sergio Polidoro},
           DOI = {10.1215/21562261-2265886},
           URL = {http://doi.org/10.1215/21562261-2265886},
    }

    PDF • DOI • Bibtex
35. Wei-Xi Li and Alberto Parmeggiani.
    Gevrey-hypoellipticity for twisted Laplacians.
    Journal of Pseudo-Differential Operators and Applications 4(2013) , 279-296

    @article {MR3089830,
        AUTHOR = {Li, Wei-Xi and Parmeggiani, Alberto},
         TITLE = {Global {G}evrey hypoellipticity for twisted {L}aplacians},
       JOURNAL = {J. Pseudo-Differ. Oper. Appl.},
      FJOURNAL = {Journal of Pseudo-Differential Operators and Applications},
        VOLUME = {4},
          YEAR = {2013},
        NUMBER = {3},
         PAGES = {279--296},
          ISSN = {1662-9981},
       MRCLASS = {35H10 (35B65 35H20)},
      MRNUMBER = {3089830},
    MRREVIEWER = {Mohammed El A\"{\i}di},
           DOI = {10.1007/s11868-013-0073-1},
           URL = {http://doi.org/10.1007/s11868-013-0073-1},
    }

    PDF • DOI • Bibtex
36. Wei-Xi Li.
    Global hypoellipticity and compactness of resolvent for Fokker-Planck operator.
    Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 11(2012), 789-815.

    @article {MR3060700,
        AUTHOR = {Li, Wei-Xi},
         TITLE = {Global hypoellipticity and compactness of resolvent for
                  {F}okker-{P}lanck operator},
       JOURNAL = {Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)},
      FJOURNAL = {Annali della Scuola Normale Superiore di Pisa. Classe di
                  Scienze. Serie V},
        VOLUME = {11},
          YEAR = {2012},
        NUMBER = {4},
         PAGES = {789--815},
          ISSN = {0391-173X},
       MRCLASS = {35H10 (47A10)},
      MRNUMBER = {3060700},
    }

    arXiv • DOI • Bibtex
37. Renjun Duan and Wei-Xi Li.
    Hypocoercivity for the linear Boltzmann equation with confining forces.
    Journal of Statistical Physics 148(2012), 306-324

    @article {MR2966364,
        AUTHOR = {Duan, Renjun and Li, Wei-Xi},
         TITLE = {Hypocoercivity for the linear {B}oltzmann equation with
                  confining forces},
       JOURNAL = {J. Stat. Phys.},
      FJOURNAL = {Journal of Statistical Physics},
        VOLUME = {148},
          YEAR = {2012},
        NUMBER = {2},
         PAGES = {306--324},
          ISSN = {0022-4715},
       MRCLASS = {35Q20 (82C40)},
      MRNUMBER = {2966364},
    MRREVIEWER = {Stephen Wollman},
           DOI = {10.1007/s10955-012-0545-3},
           URL = {https://doi.org/10.1007/s10955-012-0545-3},
    }

    arXiv • DOI • Bibtex
38. Hua Chen, Wei-Xi Li and Chao-Jiang Xu.
    Gevrey regularity of subelliptic Monge-Ampère equations in the plane.
    Advances in Mathematics 228(2011) 1816-1841.

    @article {MR2824570,
        AUTHOR = {Chen, Hua and Li, Weixi and Xu, Chaojiang},
         TITLE = {Gevrey regularity of subelliptic {M}onge-{A}mp\`ere equations in
                  the plane},
       JOURNAL = {Adv. Math.},
      FJOURNAL = {Advances in Mathematics},
        VOLUME = {228},
          YEAR = {2011},
        NUMBER = {3},
         PAGES = {1816--1841},
          ISSN = {0001-8708},
       MRCLASS = {35J96 (35A20 35B65 35H20)},
      MRNUMBER = {2824570},
    MRREVIEWER = {Jiakun Liu},
           DOI = {10.1016/j.aim.2011.06.037},
           URL = {https://doi.org/10.1016/j.aim.2011.06.037},
    }

    arXiv • DOI • Bibtex
39. Hua Chen, Wei-Xi Li and Chao-Jiang Xu.
    Gevrey hypoellipticity for a class of kinetic equations.
    Communications in Partial Differential Equations 36 (2011) 693-728.

    @article {MR2763329,
        AUTHOR = {Chen, Hua and Li, Wei-Xi and Xu, Chao-Jiang},
         TITLE = {Gevrey hypoellipticity for a class of kinetic equations},
       JOURNAL = {Comm. Partial Differential Equations},
      FJOURNAL = {Communications in Partial Differential Equations},
        VOLUME = {36},
          YEAR = {2011},
        NUMBER = {4},
         PAGES = {693--728},
          ISSN = {0360-5302},
       MRCLASS = {35H10 (35A20 35B65)},
      MRNUMBER = {2763329},
    MRREVIEWER = {Gregorio Chinni},
           DOI = {10.1080/03605302.2010.507689},
           URL = {https://doi.org/10.1080/03605302.2010.507689},
    }

    arXiv • DOI • Bibtex
40. Hua Chen, Wei-Xi Li and Chao-Jiang Xu.
    Analytic smoothness effect of solutions for spatially homogeneous Landau equation.
    Journal of Differential Equations 248 (2010) 77-94.

    @article {MR2557895,
        AUTHOR = {Chen, Hua and Li, Wei-Xi and Xu, Chao-Jiang},
         TITLE = {Analytic smoothness effect of solutions for spatially
                  homogeneous {L}andau equation},
       JOURNAL = {J. Differential Equations},
      FJOURNAL = {Journal of Differential Equations},
        VOLUME = {248},
          YEAR = {2010},
        NUMBER = {1},
         PAGES = {77--94},
          ISSN = {0022-0396},
       MRCLASS = {35B65 (35Q20 35R09 76P05 82C40)},
      MRNUMBER = {2557895},
    MRREVIEWER = {Simon Labrunie},
           DOI = {10.1016/j.jde.2009.08.006},
           URL = {https://doi.org/10.1016/j.jde.2009.08.006},
    }

    arXiv • DOI • Bibtex
41. Hua Chen, Wei-Xi Li and Chao-Jiang Xu.
    Gevrey regularity for solution of the spatially homogeneous Landau equation.
    Acta Mathematics Scientia 29(2009), 673-686.

    @article {MR2514370,
        AUTHOR = {Chen, Hua and Li, Weixi and Xu, Chaojiang},
         TITLE = {Gevrey regularity for solution of the spatially homogeneous
                  {L}andau equation},
       JOURNAL = {Acta Math. Sci. Ser. B (Engl. Ed.)},
      FJOURNAL = {Acta Mathematica Scientia. Series B. English Edition},
        VOLUME = {29},
          YEAR = {2009},
        NUMBER = {3},
         PAGES = {673--686},
          ISSN = {0252-9602},
       MRCLASS = {35R09 (35A20 35B65 35K55 82C40)},
      MRNUMBER = {2514370},
    MRREVIEWER = {Tilak Bhattacharya},
           DOI = {10.1016/S0252-9602(09)60063-1},
           URL = {https://doi.org/10.1016/S0252-9602(09)60063-1},
    }

    arXiv • DOI • Bibtex
42. Hua Chen, Wei-Xi Li and Chao-Jiang Xu.
    Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations.
    Journal of Differential Equations 246 (2009), 320- 339.

    @article {MR2467026,
        AUTHOR = {Chen, Hua and Li, Wei-Xi and Xu, Chao-Jiang},
         TITLE = {Gevrey hypoellipticity for linear and non-linear
                  {F}okker-{P}lanck equations},
       JOURNAL = {J. Differential Equations},
      FJOURNAL = {Journal of Differential Equations},
        VOLUME = {246},
          YEAR = {2009},
        NUMBER = {1},
         PAGES = {320--339},
          ISSN = {0022-0396},
       MRCLASS = {35H10 (35A20 35K55 35Q84 82C35)},
      MRNUMBER = {2467026},
    MRREVIEWER = {Fran\c{c}ois Vigneron},
           DOI = {10.1016/j.jde.2008.05.019},
           URL = {https://doi.org/10.1016/j.jde.2008.05.019},
    }

    arXiv • DOI • Bibtex
43. Hua Chen, Wei-Xi Li and Chao-Jiang Xu.
    Propagation of Gevrey regularity for solutions of Landau equations.
    Kinetic and Related Models 1(2008), 355- 368.

    @article {MR2425602,
        AUTHOR = {Chen, Hua and Li, Wei-Xi and Xu, Chao-Jiang},
         TITLE = {Propagation of {G}evrey regularity for solutions of {L}andau
                  equations},
       JOURNAL = {Kinet. Relat. Models},
      FJOURNAL = {Kinetic and Related Models},
        VOLUME = {1},
          YEAR = {2008},
        NUMBER = {3},
         PAGES = {355--368},
          ISSN = {1937-5093},
       MRCLASS = {35K55 (35A21 35B65 76P05)},
      MRNUMBER = {2425602},
    MRREVIEWER = {Svetlin Georgiev Georgiev},
           DOI = {10.3934/krm.2008.1.369},
           URL = {https://doi.org/10.3934/krm.2008.1.369},
    }

    arXiv • DOI • Bibtex
44. Shaohua Wu, Hua Chen and Wei-Xi Li.
    The local and global existence of the solutions of hyperbolic-parabolic system modeling biological phenomena.
    Acta Mathematics Scientia 28 (2008), 101- 116.

    @article {MR2389586,
        AUTHOR = {Wu, Shaohua and Chen, Hua and Li, Weixi},
         TITLE = {The local and global existence of the solutions of
                  hyperbolic-parabolic system modeling biological phenomena},
       JOURNAL = {Acta Math. Sci. Ser. B (Engl. Ed.)},
      FJOURNAL = {Acta Mathematica Scientia. Series B. English Edition},
        VOLUME = {28},
          YEAR = {2008},
        NUMBER = {1},
         PAGES = {101--116},
          ISSN = {0252-9602},
       MRCLASS = {35Q80 (35K45 35K55 35L70 47D06 92B05)},
      MRNUMBER = {2389586},
           DOI = {10.1016/S0252-9602(08)60011-9},
           URL = {https://doi.org/10.1016/S0252-9602(08)60011-9},
    }

    DOI • Bibtex
45. Wei-Xi Li and Tong Yang.
    Well-posedness in Gevrey function space for the three-dimensional Prandtl equations.
    arXiv:1708.08217. Unpublished.

     @ARTICLE{2017arXiv170808217L,
           author = {{Li}, Wei-Xi and {Yang}, Tong},
            title = "{Well-posedness in Gevrey function space for the three-dimensional Prandtl equations}",
          journal = {arXiv e-prints},
         keywords = {Mathematics - Analysis of PDEs},
             year = 2017,
            month = aug,
              eid = {arXiv:1708.08217},
            pages = {arXiv:1708.08217},
    archivePrefix = {arXiv},
           eprint = {1708.08217},
     primaryClass = {math.AP},
           adsurl = {https://ui.adsabs.harvard.edu/abs/2017arXiv170808217L},
          adsnote = {Provided by the SAO/NASA Astrophysics Data System}
    }

    arxiv • Bibtex

Collaborators & Mentors

Radjesvarane Alexandre • Hongmei Cao • Hua Chen • Jun-Ling Chen • Ke Chen • Feng Cheng • Nils Dencker • Renjun Duan • Ling-Bing He • Frédéric Hérau • Xin Hu • Jie Ji • Nicolas Lerner • Lvqiao Liu • Peng Luo • Nader Masmoudi • Van-Sang Ngo • Marius Paicu • Alberto Parmeggiani • Shuying Tian • Ling-Jun Wang • Xue Ping Wang • Yan-Lin Wang • Di Wu • Shaohua Wu • Chao-Jiang Xu • Rui Xu • Xiaojing Xu • Zhan Xu• Anita Yang •Tong Yang • Tianyuan Yu • Juan Zeng • Jinpeng Zhan • Ping Zhang