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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

Authors
  • Fan, Lili1
  • Hou, Meichen2
  • 1 Wuhan Polytechnic University, Wuhan, 430023, China , Wuhan (China)
  • 2 University of Chinese Academy of Sciences, Beijing, 100049, China , Beijing (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Oct 10, 2020
Volume
40
Issue
6
Pages
1627–1652
Identifiers
DOI: 10.1007/s10473-020-0602-y
Source
Springer Nature
Keywords
License
Yellow

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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