The Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off

作     者：Hua Chen Xin Hu Wei-Xi Li Jinpeng Zhan Hua Chen;Xin Hu;Wei-Xi Li;Jinpeng Zhan

作者机构：School of Mathematics and StatisticsWuhan UniversityWuhan 430072China Computational Science Hubei Key LaboratoryWuhan UniversityWuhan 430072China Department of MathematicsSchool of ScienceWuhan University of TechnologyWuhan 430070China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2022年第65卷第3期

页      面：443-470页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11631011) supported by National Natural Science Foundation of China(Grant Nos.11961160716,11871054 and 11771342) the Natural Science Foundation of Hubei Province(Grant No.2019CFA007) the Fundamental Research Funds for the Central Universities(Grant No.2042020kf0210) 

主　　题：Boltzmann equation Gevrey regularity subelliptic estimate non cut-off symbolic calculus 

摘      要：In this article we study the Gevrey regularization effect for the spatially inhomogeneous Boltzmann equation without angular *** equation is partially elliptic in the velocity direction and degenerates in the spatial *** consider the nonlinear Cauchy problem for the fluctuation around the Maxwellian distribution and prove that any solution with mild regularity will become smooth in the Gevrey class at positive time with the Gevrey index depending on the angular *** proof relies on the symbolic calculus for the collision operator and the global subelliptic estimate for the Cauchy problem of the linearized Boltzmann operator.