A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations

In this paper, we obtain a blow up criterion for classical solutions to the 3-D compressible Naiver-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, initial vacuum is allowed in our case.

Saved in:
Bibliographic Details
Published in:arXiv.org 2009-03
Main Authors: Huang, Xiangdi, Zhouping Xin
Format: Article
Language:English
Subjects:
Compressibility
Criteria
Fluid dynamics
Fluid flow
Incompressible flow
Mathematical analysis
Navier-Stokes equations
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we obtain a blow up criterion for classical solutions to the 3-D compressible Naiver-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, initial vacuum is allowed in our case.
ISSN:2331-8422
DOI:10.48550/arxiv.0903.3090