A Blow-Up Criterion for the Compressible Navier-Stokes equations
Mathematical Physics
2011-12-16 v1 Analysis of PDEs
math.MP
Abstract
In this paper, we obtain a blow up criterion for strong solutions to the 3-D compressible Naveri-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow. The key ingredients in our analysis are the a priori super-norm estimate of the momentum by a Moser-iteration and an estimate of the space-time square mean of the gradient of the density. In addition, initial vacuum is allowed in our case.
Keywords
Cite
@article{arxiv.0902.2606,
title = {A Blow-Up Criterion for the Compressible Navier-Stokes equations},
author = {Xiangdi Huang and Zhouping Xin},
journal= {arXiv preprint arXiv:0902.2606},
year = {2011}
}
Comments
19 pages