Year: 2026
Type: preprint
Abstract: When a uniform steady supersonic oncoming flow impinges on a straight wedge, if the wedge angle is smaller than the detachment angle, two types of steady oblique shocks satisfying the entropy condition will form in the flow field: weak shocks with supersonic or subsonic downstream flow, and strong shocks with subsonic downstream flow. There have been many results on the stability of oblique shocks with subsonic or supersonic downstream flow. However, much less is known about the stability of oblique shocks with sonic downstream flow, since the flow behind the shock wave is very sensitive to disturbances. This paper investigates the stability of oblique sonic shocks under the assumption of a straight wedge with non-uniform incoming flow. We reduce the problem to a degenerate hyperbolic free boundary problem. A local Lipschitz-continuous solution with sonic-supersonic downstream flow to the free boundary problem is constructed, using the classical Ascoli-Arzelà theorem and a diagonal argument. The main difficulty of this free boundary problem lies in the hyperbolic degeneracy on the sonic line. By adopting a weighted characteristic decomposition method, we establish a delicate estimate of the downstream flow near the sonic line.
Source: arXiv (Cornell University)
Author: Lai, Geng
Institution: Shanghai University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Award: 非线性双曲守恒律方程组的二维黎曼问题及相关问题
OpenAlex ID: W7214637950