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Asymptotic Stability of a Boundary Layer and Rarefaction Wave for the Outflow Problem of the Heat-Conductive Ideal Gas without Viscosity

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Abstract

This article is devoted to studying the initial-boundary value problem for an ideal polytropic model of non-viscous and compressible gas. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and give a rigorous proof of the asymptotic stability of both the degenerate boundary layer and its superposition with the 3-rarefaction wave under some smallness conditions. New weighted energy estimates are introduced, and the trace of the density and velocity on the boundary are handled by some subtle analysis. The decay properties of the boundary layer and the smooth rarefaction wave also play an important role.

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Acknowledgements

The authors are grateful to Professors S. Nishibata, Feimin Huang and Huijiang Zhao for their support and advice.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan, 430023, China

    Lili Fan

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Meichen Hou

Authors
  1. Lili Fan
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  2. Meichen Hou
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Corresponding authors

Correspondence to Lili Fan or Meichen Hou.

Additional information

This work was supported by the Fundamental Research grants from the Science Foundation of Hubei Province (2018CFB693). The research of L.L. Fan was supported by the Natural Science Foundation of China (11871388) and in part by the Natural Science Foundation of China (11701439).

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Fan, L., Hou, M. Asymptotic Stability of a Boundary Layer and Rarefaction Wave for the Outflow Problem of the Heat-Conductive Ideal Gas without Viscosity. Acta Math Sci 40, 1627–1652 (2020). https://doi.org/10.1007/s10473-020-0602-y

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  • DOI: https://doi.org/10.1007/s10473-020-0602-y

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