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Vanishing viscosity limit of the compressible NavierStokes equations for solutions to a Riemann problem

Feimin Huang Yi Wang Tong Yang

Analysis of PDEs mathscidoc:1912.43755

Archive for Rational Mechanics and Analysis, 203, (2), 379-413, 2012.2
We study the vanishing viscosity limit of the compressible NavierStokes equations to the Riemann solution of the Euler equations that consists of the superposition of a shock wave and a rarefaction wave. In particular, it is shown that there exists a family of smooth solutions to the compressible NavierStokes equations that converges to the Riemann solution away from the initial and shock layers at a rate in terms of the viscosity and the heat conductivity coefficients. This gives the first mathematical justification of this limit for the NavierStokes equations to the Riemann solution that contains these two typical nonlinear hyperbolic waves.
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@inproceedings{feimin2012vanishing,
  title={Vanishing viscosity limit of the compressible NavierStokes equations for solutions to a Riemann problem},
  author={Feimin Huang, Yi Wang, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205537826639319},
  booktitle={Archive for Rational Mechanics and Analysis},
  volume={203},
  number={2},
  pages={379-413},
  year={2012},
}
Feimin Huang, Yi Wang, and Tong Yang. Vanishing viscosity limit of the compressible NavierStokes equations for solutions to a Riemann problem. 2012. Vol. 203. In Archive for Rational Mechanics and Analysis. pp.379-413. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205537826639319.
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