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Global well-posedness of 2D compressible NavierStokes equations with large data and vacuum

Quansen Jiu Yi Wang Zhouping Xin

Analysis of PDEs mathscidoc:1912.43750

Journal of Mathematical Fluid Mechanics, 16, (3), 483-521, 2014.9
In this paper, we study the global well-posedness of the 2D compressible NavierStokes equations with large initial data and vacuum. It is proved that if the shear viscosity<i></i> is a positive constant and the bulk viscosity <i></i> is the power function of the density, that is, <i></i>(<i></i>) = <i></i> <sup> <i></i> </sup> with <i></i> &gt; 3, then the 2D compressible NavierStokes equations with the periodic boundary conditions on the torus T 2 admit a unique global classical solution (<i>, u</i>) which may contain vacuums in an open set of T 2 . Note that the initial data can be arbitrarily large to contain vacuum states.
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@inproceedings{quansen2014global,
  title={Global well-posedness of 2D compressible NavierStokes equations with large data and vacuum},
  author={Quansen Jiu, Yi Wang, and Zhouping Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205518996537314},
  booktitle={Journal of Mathematical Fluid Mechanics},
  volume={16},
  number={3},
  pages={483-521},
  year={2014},
}
Quansen Jiu, Yi Wang, and Zhouping Xin. Global well-posedness of 2D compressible NavierStokes equations with large data and vacuum. 2014. Vol. 16. In Journal of Mathematical Fluid Mechanics. pp.483-521. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205518996537314.
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