二维定常Chaplygin气体绕直楔流动

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1270-1282.

二维定常Chaplygin气体绕直楔流动

贾嘉()

^{华东师范大学数学科学学院上海 200241}

收稿日期:2020-07-29 出版日期:2021-10-26 发布日期:2021-10-08
作者简介:贾嘉, E-mail: jmjvictory@163.com

The Two-Dimensional Steady Chaplygin Gas Flows Passing a Straight Wedge

Jia Jia()

^{School of Mathematical Sciences, East China Normal University, Shanghai 200241}

Received:2020-07-29 Online:2021-10-26 Published:2021-10-08

摘要/Abstract

摘要：

该文主要研究二维定常超音速Chaplygin气体绕直楔流动, 在Radon测度解的定义下得到了Mach数大于1的所有情况解的精确表达式. 与多方气体不同, 对Chaplygin气体绕流问题, 存在Mach数$ M^{\ast}_{0} $, 当来流Mach数大于或等于该数时, 质量会在楔表面集中, 此时, 没有Lebesgue意义下的分片光滑解. 该文通过极限分析, 证明了由Lebesgue积分意义下得到的极限与Radon测度解意义下求得的解是一致的.

关键词: Chaplygin气体, Radon测度解, Riemann问题, 高超音速极限

Abstract:

The purpose of this paper is to investigate the two-dimensional steady supersonic chaplygin gas flows passing a straight wedge. By the definition of Radon measure solution, the accurate expressions are obtained for all cases where the Mach number is greater than 1. It is quite different from the polytropic gas, for the chaplygin gas flows passing problems, there exists a Mach number $ M^{\ast}_{0} $, when the Mach number of incoming flows is greater than or equal to $ M^{\ast}_{0} $, the quality will be concentrated on the surface of the straight wedge. At this time, there are not piecewise smooth solutions in the Lebesgue sense. The limit analysis is used to prove that the limit obtained by Lebesgue integral is consistent with the solution obtained in the sence of Radon measure solution.

Key words: Chaplygin gas, Radon measure solution, Riemann problem, Hypersonic limit

中图分类号:

O175.2

贾嘉. 二维定常Chaplygin气体绕直楔流动[J]. 数学物理学报, 2021, 41(5): 1270-1282.

Jia Jia. The Two-Dimensional Steady Chaplygin Gas Flows Passing a Straight Wedge[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1270-1282.

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