AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (230.2 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Global solutions to a nonlinear Fokker-Planck equation

Xingang Zhang1, Zhe Liu2, Ling Ding3, Bo Tang3,4( )
School of Computer Science and Technology, Nanyang Normal University, Nanyang, Henan 473061, China
Nanyang Normal University, Nanyang, Henan 473061, China
School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang, Hubei 441053, China
Hubei Key Laboratory of Power System Design and Test for Electrical Vehicle, Hubei University of Arts and Science, Xiangyang, Hubei 441053, China
Show Author Information

Abstract

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 x 2 L v 2 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.

Keywords

nonlinear Fokker-Planck equationglobal existenceenergy methodCauchy problemPriori estimates
CLC number: 35A01, 35Q84

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 16115-16126
DOI: 10.3934/math.2023822

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Zhang X, Liu Z, Ding L, et al. Global solutions to a nonlinear Fokker-Planck equation. AIMS Mathematics, 2023, 8(7): 16115-16126. https://doi.org/10.3934/math.2023822

3

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 22 October 2022
Revised: 21 January 2023
Accepted: 17 March 2023
Published: 15 July 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)