文献类型：期刊文献

英文题名：Global Existence and Decay Rates of the Solutions Near Maxwellian for Non-linear Fokker-Planck Equations

作者：Liao, Jie[1];Wang, Qianrong[1];Yang, Xiongfeng[2]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Shanghai Jiao Tong Univ, Sch Math Sci, Key Lab Sci & Engn Comp MOE, Shanghai 200240, Peoples R China

年份：2018

卷号：173

期号：1

起止页码：222

外文期刊名：JOURNAL OF STATISTICAL PHYSICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000445915700010)】；

基金：J. Liao would like thank Professor R. Alexandre for many valuable discussions on the model. This research is partially supported by Fundamental Research Funds for the Central Universities. X.F. Yang is supported by National Science Fund of China under the Grant 11171212 and the SJTU's SMC Projection. The detailed suggestions from the anonymous referees are greatly appreciated.

语种：英文

外文关键词：Non-linear Fokker-Planck equation; Global existence; Decay rates; Uniform-in-time estimates

摘要：In this paper, we study the global existence and decay rates of the solutions near Maxwellian for non-linear Fokker-Planck equations in the whole space. The global existence is proved by combining uniform-in-time energy estimates with local solution constructed by Picard type iteration sequence. The decay rates of the nonlinear model is obtained by using the precise spectral analysis of the linearized Fokker-Planck operator as well as the energy method. The nonlinearity in the model brings new difficulty to the energy estimates, which is resolved by additional tailored weighted-in-v energy estimates suitable for Fokker-Planck operators.