ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY∗

doi:10.1007/s10473-023-0417-8

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (4): 1735-1766.doi: 10.1007/s10473-023-0417-8

ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY^∗

Lili FAN¹, Meichen HOU^2,3,†

1. School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China;
2. School of Mathematics and CNS, Northwest University, Xi'an 710069, China;
3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2022-04-15 发布日期:2023-08-08
通讯作者: †Meichen HOU, E-mail: meichenhou@nwu.edu.cn
作者简介:Lili FAN, E-mail: fll810@live.cn
基金资助:
* Fan's research was supported by the Natural Science Foundation of China (11871388).

ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY^∗

Lili FAN¹, Meichen HOU^2,3,†

1. School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China;
2. School of Mathematics and CNS, Northwest University, Xi'an 710069, China;
3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2022-04-15 Published:2023-08-08
Contact: †Meichen HOU, E-mail: meichenhou@nwu.edu.cn
About author:Lili FAN, E-mail: fll810@live.cn
Supported by:
* Fan's research was supported by the Natural Science Foundation of China (11871388).

摘要/Abstract

摘要： This paper is concerned with an ideal polytropic model of non-viscous and heat-conductive gas in a one-dimensional half space. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and we prove the stability of the viscous shock wave and its superposition with the boundary layer under some smallness conditions. Our waves occur in the subsonic area. The intrinsic properties of our system are more challenging in mathematical analysis, however, in the subsonic area, the lack of a boundary condition on the density provides us with a special manner for defining the shift for the viscous shock wave, and helps us to construct the asymptotic profiles successfully. New weighted energy estimates are introduced and the perturbations on the boundary are handled by some subtle estimates.

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

Abstract: This paper is concerned with an ideal polytropic model of non-viscous and heat-conductive gas in a one-dimensional half space. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and we prove the stability of the viscous shock wave and its superposition with the boundary layer under some smallness conditions. Our waves occur in the subsonic area. The intrinsic properties of our system are more challenging in mathematical analysis, however, in the subsonic area, the lack of a boundary condition on the density provides us with a special manner for defining the shift for the viscous shock wave, and helps us to construct the asymptotic profiles successfully. New weighted energy estimates are introduced and the perturbations on the boundary are handled by some subtle estimates.

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

Lili FAN, Meichen HOU. ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1735-1766.

Lili FAN, Meichen HOU. ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY^∗[J]. Acta mathematica scientia,Series B, 2023, 43(4): 1735-1766.

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ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY^∗

ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY^∗

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