Gevrey Hypoellipticity for a Class of Kinetic Equations

DOI10.1080/03605302.2010.507689zbMath1242.35103arXiv1102.5432OpenAlexW1998186542MaRDI QIDQ3104526

Hua Chen, Wei-Xi Li, Chao-Jiang Xu

Publication date: 14 December 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.5432

zbMATH Keywords

Fourier multiplierssemilinear equationsGevrey classes

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Hypoelliptic equations (35H10) Boltzmann equations (35Q20)

Related Items (16)

Fundamental solutions of nonlocal Hörmander's operators ⋮ The resolvent of the linearized Boltzmann operator with a stationary potential ⋮ Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff ⋮ Analytic smoothing effect of the spatially inhomogeneous Landau equations for hard potentials ⋮ Gevrey regularity of subelliptic Monge-Ampère equations in the plane ⋮ Existence and analytic regularity of certain solutions for the generalized BBM-Burgers equation in $\mathbb R^n$ ⋮ Hypoelliptic Estimates for a Linear Model of the Boltzmann Equation Without Angular Cutoff ⋮ Phase space analysis of semilinear parabolic equations ⋮ Global hypoelliptic estimates for fractional order kinetic equation ⋮ Global existence and full regularity of the Boltzmann equation without angular cutoff ⋮ The Boltzmann equation without angular cutoff in the whole space: qualitative properties of solutions ⋮ Gevrey Class Smoothing Effect for the Prandtl Equation ⋮ Well-posedness in Sobolev spaces of the two-dimensional MHD boundary layer equations without viscosity ⋮ Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation ⋮ Analyticity of rotational traveling capillary-gravity waves with critical layers ⋮ The Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off

Cites Work

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• Ultra-analytic effect of Cauchy problem for a class of kinetic equations
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• Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians
• Isotropic hypoelliptic and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
• Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations
• Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff
• Propagation of Gevrey regularity for solutions of the Boltzmann equation for Maxwellian molecules
• Local solutions in gevrey classes to the nonlinear Boltzmann equation without cutoff
• LITTLEWOOD–PALEY THEORY AND REGULARITY ISSUES IN BOLTZMANN HOMOGENEOUS EQUATIONS I: NON-CUTOFF CASE AND MAXWELLIAN MOLECULES

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