Two-dimensional pseudo-steady supersonic flow around a sharp corner for the generalized Chaplygin gas

AIMS Mathematics

article

Aidi Yao¹ 

[1]School of Mathematics and Big Data, Anhui University of Science and Technology

关键词: two-dimensional Euler equations;    generalized Chaplygin gas;    pseudo-steady supersonic flow;    incomplete centered simple wave;    interaction of simple wave with rigid wall boundary;   

DOI  :  10.3934/math.2022654

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper, the expansion problem which arises in a two-dimensional (2D) isentropic pseudo-steady supersonic flow expanding into vacuum around a sharp corner for the generalized Chaplygin gas is studied. This expanding problem catches the interaction of an incomplete centered simple wave with a backward planar rarefaction wave and the interaction of a non-planar simple wave with a rigid wall boundary of the 2D self-similar Euler equations. Using the methods of characteristic decompositions and invariant regions, we get the hyperbolicity in the wave interaction domains and prior $ C^{1} $ estimates of solutions to the two interaction problems. It follows the global existence of the solution up to infinity of the gas expansion problem.

【 授权许可】

CC BY