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 Communications in Analysis and Mechanics Article
PDF (395.7 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

Well-posedness of classical solutions to the 3D isentropic compressible Navier-Stokes-Poisson equations with degenerate viscosities and vacuum

Peng Lu1( ), Shaojun Yu2
Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, P.R. China
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, P.R. China
Show Author Information

Abstract

We consider the isentropic compressible Navier-Stokes-Poisson equations with degenerate viscosities and vacuum in a three-dimensional torus. The local well-posedness of classical solution is established by introducing a "quasi-symmetric hyperbolic"–"degenerate elliptic" coupled structure to control the behavior of the velocity of the fluid near the vacuum and give some uniform estimates. In particular, the initial data allows vacuum in an open set and we do not need any initial compatibility conditions.

Keywords

density-dependent viscositiescompressible Navier-Stokes-Poisson equationsvacuumlocal well-posednessclassical solutions
CLC number: 35Q35, 35A09, 76N10

References

【1】
【1】
 
 
Crossref Google Scholar
Communications in Analysis and Mechanics
Volume 17 Issue 3,
September 2025
Pages 779-809
DOI: 10.3934/cam.2025031

{{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:
Lu P, Yu S. Well-posedness of classical solutions to the 3D isentropic compressible Navier-Stokes-Poisson equations with degenerate viscosities and vacuum. Communications in Analysis and Mechanics, 2025, 17(3): 779-809. https://doi.org/10.3934/cam.2025031

0

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 08 May 2025
Revised: 25 August 2025
Accepted: 27 August 2025
Published: 15 September 2025
©2025 the Author(s), licensee AIMS Press.

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