文献类型：期刊文献

英文题名：Stability of Global Maxwellian for Fully Nonlinear Fokker-Planck Equations

作者：Liao, Jie[1];Yang, Xiongfeng[2,3]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China;[2]Shanghai Jiao Tong Univ, Sch Math Sci, MOE LSC, Shanghai 200240, Peoples R China;[3]Shanghai Jiao Tong Univ, Sch Math Sci, SHL MAC, Shanghai 200240, Peoples R China

年份：2021

卷号：185

期号：3

外文期刊名：JOURNAL OF STATISTICAL PHYSICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000716446200002)】；

基金：The authors would like to thank the anonymous referees for their kind suggestions. This research is partially supported by National Natural Science Foundation of China (Nos. 11871335 and 11971008).

语种：英文

外文关键词：Non-linear Fokker-Planck equation; Macro-micro decomposition; Global a priori estimates; Global Maxwellian

摘要：This paper considers the stability of solutions around a global Maxwellian to the fully non-linear Fokker-Planck equation in the whole space. This model preserves mass, momentum and energy at the same time, and its dissipation is much weaker than that in the simplified model considered in Liao et al. (J Stat Phys 173:222-241, 2018). To overcome the new difficulties, the macro-micro decomposition of the solution around the local Maxwellian and energy estimates introduced in Liu et al. (Physica D 188:178-192, 2004) and Yang and Zhao (J Math Phys 47:053301, 2006) for Boltzmann equation is used. That is, we reformulate the model into a fluid-type system coupled with an equation of the microscopic part. The a priori estimates of the solution could be obtained by the standard energy method. Especially, by careful computation, the viscosity and heat diffusion terms in the fluid-type system are derived from the microscopic part, which give the dissipative mechanism to the system.