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Zero dissipation limit of the compressible heat-conducting Navier-Stokes equations in the presence of the shock

Yi Wang

Analysis of PDEs mathscidoc:1912.43759

Acta Mathematica Scientia, 28, (4), 727-748, 2008.10
The zero dissipation limit of the compressible heat-conducting NavierStokes equations in the presence of the shock is investigated. It is shown that when the heat conduction coefficient and the viscosity coefficient satisfy = O (), = O (), c> 0, as 0 (see (1.3)), if the solution of the corresponding Euler equations is piecewise smooth with shock wave satisfying the Lax entropy condition, then there exists a smooth solution to the NavierStokes equations, which converges to the piecewise smooth shock solution of the Euler equations away from the shock discontinuity at a rate of . The proof is given by a combination of the energy estimates and the matched asymptotic analysis introduced in [3].
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@inproceedings{yi2008zero,
  title={Zero dissipation limit of the compressible heat-conducting Navier-Stokes equations in the presence of the shock},
  author={Yi Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205550544119323},
  booktitle={Acta Mathematica Scientia},
  volume={28},
  number={4},
  pages={727-748},
  year={2008},
}
Yi Wang. Zero dissipation limit of the compressible heat-conducting Navier-Stokes equations in the presence of the shock. 2008. Vol. 28. In Acta Mathematica Scientia. pp.727-748. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205550544119323.
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