The Gevrey hypoellipticity for kinetic equations
Hua Chen, Weixi Li, Chao-Jiang Xu (LMRS)
TL;DR
This paper investigates the Gevrey regularity of weak solutions to certain linear and semi-linear kinetic equations, providing insights into the smoothness properties of solutions related to the Boltzmann equation without angular cutoff.
Contribution
It establishes Gevrey hypoellipticity results for kinetic equations modeling inhomogeneous Boltzmann equations without angular cutoff, advancing understanding of solution regularity.
Findings
Proves Gevrey regularity for weak solutions
Extends hypoellipticity results to kinetic equations without angular cutoff
Provides a framework for analyzing smoothness in kinetic models
Abstract
In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.
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