Global solutions to a nonlinear Fokker-Planck equation

被引：0

作者：

Zhang, Xingang ^{[1
]}

Liu, Zhe ^{[2
]}

Ding, Ling ^{[3
]}

Tang, Bo ^{[3
,4
]}

机构：

[1] Nanyang Normal Univ, Sch Comp Sci & Technol, Nanyang 473061, Henan, Peoples R China

[2] Nanyang Normal Univ, Nanyang 473061, Henan, Peoples R China

[3] Hubei Univ Arts & Sci, Sch Math & Stat, Xiangyang 441053, Hubei, Peoples R China

[4] Hubei Univ Arts & Sci, Hubei Key Lab Power Syst Design & Test Elect Vehic, Xiangyang 441053, Hubei, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 07期

基金：

中国国家自然科学基金;

关键词：

nonlinear Fokker-Planck equation; global existence; energy method; Cauchy problem; Priori estimates; CLASSICAL-SOLUTIONS; BOLTZMANN-EQUATION; EXISTENCE;

D O I：

10.3934/math.2023822

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we construct global solutions to the Cauchy problem on a nonlinear Fokker -Planck equation near Maxwellian with small-amplitude initial data in Sobolev space Hx2L2v by a refined nonlinear energy method. Compared with the results of Liao et al. (Global existence and decay rates of the solutions near Maxwellian for non-linear Fokker-Planck equations, J. Stat. Phys., 173 (2018), 222-241.), the regularity assumption on the initial data is much weaker.

引用

页码：16115 / 16126

页数：12

共 19 条

[1]

Adams R.A., 2003, Sobolev Spaces, Vsecond

[2]

[Anonymous], 1988, BOLTZMANN EQUATION I

[3] GLOBAL CLASSICAL SOLUTIONS CLOSE TO EQUILIBRIUM TO THE VLASOV-FOKKER-PLANCK-EULER SYSTEM [J].