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Research Topics


Partial Differential Equations and Mathematical Physics


  • Spectral theory. Fokker-Planck operator, Witten Laplacian, Non-selfadjoint Schrödinger operator, Compact resolvent, global hypoellipticity,
  • Boundary layer analysis for fluid mechanics equations. Prandtl boundary layer, inviscid limit of Navier-Stokes equation, Gevrey class
  • Regularity of degenerate elliptic equations. Boltzmann equation, Monge-Ampère equations, twisted Laplacians, subelliptic estimate

Publications

MathSciNet


  1. Hua Chen, Xin Hu, Wei-Xi Li and Jinpeng Zhan
    Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off
    Preprint, arXiv:1805.12543 [ abstract / arXiv ]
  2. Hua Chen, Xin Hu, Wei-Xi Li and Jinpeng Zhan
    The resolvent of the linearized Boltzmann operator with a confining potential
    Preprint [ abstract / PDF ]
  3. Wei-Xi Li and Tong Yang
    Well-posedness in Gevrey function space for the three-dimensional Prandtl equations
    Preprint, arXiv:1708.08217 [ abstract / doi / arXiv ]
  4. Wei-Xi Li,Van-Sang Ngo and Chao-Jiang Xu
    Boundary layer analysis for the fast horizontal rotating fluids
    Preprint, arXiv:1611.04896 [ abstract / doi / arXiv ]
  5. Radjesvarane Alexandre, Frédéric Hérau and Wei-Xi Li
    Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff.
    Preprint, arXiv:1212.4632 [ abstract / doi / arXiv ]
  6. Wei-Xi Li
    Spectral Analysis for Fokker-Planck operator and Witten Laplacian(in Chinese), in Honor of the 90th birthday of Professor Minyou Qi.
    Accepted by SCIENTIA SINICA Mathematica ( 中国科学:数学) [ abstract / PDF ]
  7. Wei-Xi Li and Tong Yang
    Well-posedness in Gevrey function space for the Prandtl equations with non-degenerate critical points.
    Accepted by Journal of the European Mathematical Society (JEMS) [ abstract / doi / arXiv ]
  8. 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 [ abstract / doi / arXiv ]
  9. Wei-Xi Li
    Compactness of the resolvent for the Witten Laplacian
    Annales Henri Poincaré 19 (2018), 1259–1282 [ abstract / doi / arXiv ]
  10. Wei-Xi Li
    Compactness criteria for the resolvent of the Fokker-Planck operator.
    Ann. Sc. Norm. Super. Pisa Cl. Sci. Vol. XVIII, issue 1 (2018), 119-143 [ abstract / doi / arXiv ]
  11. 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 [ abstract / doi / pdf ]
  12. 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 [ abstract / doi / arXiv ]

  13. 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
  14. Wei-Xi Li, Di Wu and Chao-Jiang Xu
    Gevrey Class Smoothing Effect for the Prandtl Equation.
    SIAM J. Math. Anal. 48 (2016),1672–1726
  15. Wei-Xi Li
    Global hypoelliptic estimates for fractional order kinetic equation.
    Mathematische Nachrichten 287(2014), 610-637
  16. Wei-Xi Li and Alberto Parmeggiani
    Gevrey-hypoellipticity for twisted Laplacians.
    Journal of Pseudo-Differential Operators and Applications 4(2013), 279-296
  17. 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
  18. Frédéric Hérau and Wei-Xi Li
    Global hypoelliptic estimates for Landau-type operator with external potential.
    Kyoto J. Math 53 (2013), 533-565
  19. Renjun Duan and Wei-Xi Li
    Hypocoercivity for the linear Boltzmann equation with confining forces.
    Journal of Statistical Physics 148(2012), 306-324
  20. Wei-Xi Li
    Global hypoellipticity and compactness of resolvent for Fokker-Planck operator.
    Ann. Sc. Norm. Super. Pisa Cl. Sci. Vol. XI(2012), 789-815.
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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.

Collaborators & Mentors



Radjesvarane Alexandre / Hua Chen / Feng Cheng / Nils Dencker / Renjun Duan / Frédéric Hérau / Xin Hu / Nicolas Lerner / Peng Luo / Van-Sang Ngo / Alberto Parmeggiani / Shuying Tian / Ling-Jun Wang / Xue Ping Wang / Yan-Lin Wang / Di Wu / Shaohua Wu / Chao-Jiang Xu / Tong Yang / Jinpeng Zhan