Existence and blowup behavior of global strong solutions to the two-dimensional barotropic compressible Navier–Stokes system with vacuum and large initial data

Xiangdi Huang Institute of Mathematics, Academy of Mathematics and Systems Science

Analysis of PDEs mathscidoc:1803.03003

J. Math. Pures Appl., 106, (1), 123–154, 2016.2
For periodic initial data with density allowed to vanish initially, we establish the global existence of strong and weak solutions to the two-dimensional barotropic compressible Navier–Stokes equations with no restrictions on the size of initial data provided the shear viscosity is a positive constant and the bulk one is λ =ρ^β with β>4/3. These results generalize and improve the previous ones due to Vaigant–Kazhikhov [Sib. Math. J. 36 (1995) 1283–1316] who required β>3. Moreover, we also prove that the densities for both the strong and weak solutions remain bounded from above independently of time. As a consequence, it is shown that both the strong and weak solutions converge to the equilibrium state as time tends to infinity.
Compressible Navier-Stokes equations; Global strong solution
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@inproceedings{xiangdi2016existence,
  title={Existence and blowup behavior of global strong solutions to the two-dimensional barotropic compressible Navier–Stokes system with vacuum and large initial data},
  author={Xiangdi Huang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180302113452803705959},
  booktitle={J. Math. Pures Appl.},
  volume={106},
  number={1},
  pages={123–154},
  year={2016},
}
Xiangdi Huang. Existence and blowup behavior of global strong solutions to the two-dimensional barotropic compressible Navier–Stokes system with vacuum and large initial data. 2016. Vol. 106. In J. Math. Pures Appl.. pp.123–154. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180302113452803705959.
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