## 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

- 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 ] - Hua
Chen, Xin Hu, Wei-Xi Li and Jinpeng Zhan

The resolvent of the linearized Boltzmann operator with a confining potential

Preprint [ abstract / PDF ] - 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 ] - 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 ] - 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 ] - 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 ] - 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 ] - 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 ] - Wei-Xi Li

Compactness of the resolvent for the Witten Laplacian

Annales Henri Poincaré 19 (2018), 1259–1282 [ abstract / doi / arXiv ] - 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 ] - 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 ] - 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 ] - 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 - 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 - Wei-Xi Li

Global hypoelliptic estimates for fractional order kinetic equation.

Mathematische Nachrichten 287(2014), 610-637 - Wei-Xi Li and Alberto
Parmeggiani

Gevrey-hypoellipticity for twisted Laplacians.

Journal of Pseudo-Differential Operators and Applications 4(2013), 279-296 - 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 - Frédéric
Hérau and Wei-Xi Li

Global hypoelliptic estimates for Landau-type operator with external potential.

Kyoto J. Math 53 (2013), 533-565 - Renjun
Duan and Wei-Xi Li

Hypocoercivity for the linear Boltzmann equation with confining forces.

Journal of Statistical Physics 148(2012), 306-324 - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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