ASYMPTOTIC STABILITY OF A BOUNDARY LAYER AND RAREFACTION WAVE FOR THE OUTFLOW PROBLEM OF THE HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY

doi:10.1007/s10473-020-0602-y

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (6): 1627-1652.doi: 10.1007/s10473-020-0602-y

ASYMPTOTIC STABILITY OF A BOUNDARY LAYER AND RAREFACTION WAVE FOR THE OUTFLOW PROBLEM OF THE HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY

范丽丽¹, 侯美晨²

1. School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China;
2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2019-10-07 修回日期:2020-07-31 出版日期:2020-12-25 发布日期:2020-12-30
作者简介:Lili FAN,E-mail:fll810@live.cn;Meichen HOU,E-mail:meichenhou@amss.ac.cn
基金资助:
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).

ASYMPTOTIC STABILITY OF A BOUNDARY LAYER AND RAREFACTION WAVE FOR THE OUTFLOW PROBLEM OF THE HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY

Lili FAN¹, Meichen HOU²

1. School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China;
2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2019-10-07 Revised:2020-07-31 Online:2020-12-25 Published:2020-12-30
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: non-viscous, degenerate boundary layer, rarefaction wave, outflow problem

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.

Key words: non-viscous, degenerate boundary layer, rarefaction wave, outflow problem

中图分类号:

35B35

范丽丽, 侯美晨. ASYMPTOTIC STABILITY OF A BOUNDARY LAYER AND RAREFACTION WAVE FOR THE OUTFLOW PROBLEM OF THE HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY[J]. 数学物理学报(英文版), 2020, 40(6): 1627-1652.

Lili FAN, Meichen HOU. ASYMPTOTIC STABILITY OF A BOUNDARY LAYER AND RAREFACTION WAVE FOR THE OUTFLOW PROBLEM OF THE HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY[J]. Acta mathematica scientia,Series B, 2020, 40(6): 1627-1652.

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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

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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