Zero dissipation limit to rarefaction wave with vacuum for one-dimensional compressible NavierStokes equations

Feimin Huang Mingjie Li Yi Wang

Analysis of PDEs mathscidoc:1912.43760

SIAM Journal on Mathematical Analysis, 44, (3), 1742-1759, 2012.5
It is well-known that one-dimensional isentropic gas dynamics has two elementary waves, i.e., shock wave and rarefaction wave. Among the two waves, only the rarefaction wave can be connected to a vacuum. Given a rarefaction wave with one-side vacuum state to the compressible Euler equations, we can construct a sequence of solutions to one-dimensional compressible isentropic NavierStokes equations which converge to the above rarefaction wave with vacuum as the viscosity tends to zero. Moreover, the uniform convergence rate is obtained. The proof consists of a scaling argument and elementary energy analysis based on the underlying rarefaction wave structures.
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@inproceedings{feimin2012zero,
  title={Zero dissipation limit to rarefaction wave with vacuum for one-dimensional compressible NavierStokes equations},
  author={Feimin Huang, Mingjie Li, and Yi Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205553828634324},
  booktitle={SIAM Journal on Mathematical Analysis},
  volume={44},
  number={3},
  pages={1742-1759},
  year={2012},
}
Feimin Huang, Mingjie Li, and Yi Wang. Zero dissipation limit to rarefaction wave with vacuum for one-dimensional compressible NavierStokes equations. 2012. Vol. 44. In SIAM Journal on Mathematical Analysis. pp.1742-1759. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205553828634324.
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