NavierStokes equations with degenerate viscosity, vacuum and gravitational force

Renjun Duan Tong Yang Changjiang Zhu

Analysis of PDEs mathscidoc:1912.43986

Mathematical methods in the applied sciences, 30, (3), 347-374, 2007.2
The global existence of weak solutions to the compressible NavierStokes equations with vacuum attracts many research interests nowadays. For the isentropic gas, the viscosity coefficient depends on density function from physical point of view. When the density function connects to vacuum continuously, the vacuum degeneracy gives some analytic difficulties in proving global existence. In this paper, we consider this case with gravitational force and fixed boundary condition. By giving a series of <i>a priori</i> estimates on the solution coping with the degeneracy of vacuum, gravitational force and boundary effect, we give global existence and uniqueness results similar to the case without force and boundary. Copyright 2006 John Wiley &amp; Sons, Ltd.
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@inproceedings{renjun2007navierstokes,
  title={NavierStokes equations with degenerate viscosity, vacuum and gravitational force},
  author={Renjun Duan, Tong Yang, and Changjiang Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211055270650550},
  booktitle={Mathematical methods in the applied sciences},
  volume={30},
  number={3},
  pages={347-374},
  year={2007},
}
Renjun Duan, Tong Yang, and Changjiang Zhu. NavierStokes equations with degenerate viscosity, vacuum and gravitational force. 2007. Vol. 30. In Mathematical methods in the applied sciences. pp.347-374. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211055270650550.
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