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Vanishing viscosity of isentropic Navier-Stokes equations for interacting shocks

FeiMin Huang Yi Wang Yong Wang Tong Yang

Analysis of PDEs mathscidoc:1912.43762

Science China Mathematics, 58, (4), 653-672, 2015.4
We study the vanishing viscosity of the Navier-Stokes equations for interacting shocks. Given an entropy solution to <i>p</i>-system which consists of two different families of shocks interacting at some positive time, we show that such entropy solution is the vanishing viscosity limit of a family of global smooth solutions to the isentropic Navier-Stokes equations. The key point of the proofs is to derive the estimates separately before and after the interaction time and connect the incoming and outgoing viscous shock profiles.
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@inproceedings{feimin2015vanishing,
  title={Vanishing viscosity of isentropic Navier-Stokes equations for interacting shocks},
  author={FeiMin Huang, Yi Wang, Yong Wang, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205600066791326},
  booktitle={Science China Mathematics},
  volume={58},
  number={4},
  pages={653-672},
  year={2015},
}
FeiMin Huang, Yi Wang, Yong Wang, and Tong Yang. Vanishing viscosity of isentropic Navier-Stokes equations for interacting shocks. 2015. Vol. 58. In Science China Mathematics. pp.653-672. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205600066791326.
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