Compressible NavierStokes equations with degenerate viscosity coefficient and vacuum

Tong Yang Changjiang Zhu

Analysis of PDEs mathscidoc:1912.43927

Communications in Mathematical Physics, 230, (2), 329-363, 2002.10
In this paper, we consider the compressible NavierStokes equations for isentropic flow of finite total mass when the initial density is either of compact or infinite support. The viscosity coefficient is assumed to be a power function of the density so that the Cauchy problem is well-posed. New global existence results are established when the density function connects to the vacuum states continuously. For this, some new <i>a priori</i> estimates are obtained to take care of the degeneracy of the viscosity coefficient at vacuum. We will also give a non-global existence theorem of regular solutions when the initial data are of compact support in Eulerian coordinates which implies singularity forms at the interface separating the gas and vacuum.
No keywords uploaded!
[ Download ] [ 2019-12-24 21:07:17 uploaded by Tong_Yang ] [ 341 downloads ] [ 0 comments ]
@inproceedings{tong2002compressible,
  title={Compressible NavierStokes equations with degenerate viscosity coefficient and vacuum},
  author={Tong Yang, and Changjiang Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210717653188491},
  booktitle={Communications in Mathematical Physics},
  volume={230},
  number={2},
  pages={329-363},
  year={2002},
}
Tong Yang, and Changjiang Zhu. Compressible NavierStokes equations with degenerate viscosity coefficient and vacuum. 2002. Vol. 230. In Communications in Mathematical Physics. pp.329-363. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210717653188491.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved