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.
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页码：16115 / 16126
页数：12
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