Spectrum structure and decay rate estimates on the Landau equation with Coulomb potential

作     者：Tong Yang Hongjun Yu 

作者机构：Department of MathematicsCity University of Hong KongHong KongChina School of Mathematical SciencesSouth China Normal UniversityGuangzhou 510631China 

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

年 卷 期：2023年第66卷第1期

页      面：37-78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 the Research Grants Council of the Hong Kong Special Administrative Region of the People’s Republic of China (Grant No.SRF2021-1S01) National Natural Science Foundation of China (Grant No.11971200) supported by National Natural Science Foundation of China (Grant No.11871229) the Project Supported by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme 2017 

主　　题：spectrum structure time decay rate Landau equation Boltzmann equation 

摘      要：In this paper we first deduce the estimates on the linearized Landau operator with Coulomb potential and then analyze its spectrum structure by using semigroup theory and linear operator perturbation *** on these estimates,we give the precise time decay rate estimates on the semigroup generated by the linearized Landau operator so that the optimal time decay rates of the nonlinear Landau equation *** addition,we present a similar result for the non-angular cutoff Boltzmann equation with soft potentials.