Global solutions to a nonlinear Fokker-Planck equation-Reference-Cited by-同舟云学术

Global solutions to a nonlinear Fokker-Planck equation

Published:2023 Issue:7 Volume:8 Page:16115-16126
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Zhang Xingang¹,Liu Zhe²,Ding Ling³,Tang Bo³⁴

Affiliation:

1. School of Computer Science and Technology, Nanyang Normal University, Nanyang, Henan 473061, China

2. Nanyang Normal University, Nanyang, Henan 473061, China

3. School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang, Hubei 441053, China

4. Hubei Key Laboratory of Power System Design and Test for Electrical Vehicle, Hubei University of Arts and Science, Xiangyang, Hubei 441053, China

Abstract

<abstract><p>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 $ H^2_{x}L^2_v $ 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, <italic>J. Stat. Phys.</italic>, <bold>173</bold> (2018), 222–241.), the regularity assumption on the initial data is much weaker.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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