Shock Interaction in Plane Symmetry

TL;DR

This paper analyzes the complex interaction of two shocks in a plane symmetric barotropic fluid, establishing local solutions post-interaction and addressing a challenging double free boundary problem.

Contribution

It extends previous work on shock reflection to the more complex scenario of shock-shock interaction, providing new mathematical insights into the problem.

Findings

Established local in time solutions after shock interaction

Determined the state behind the emerging shocks

Addressed the double free boundary problem with limited initial data

Abstract

We consider the problem of interaction of two oncoming shocks in plane symmetry for a barotropic fluid. We establish a local in time solution after the point of interaction, thereby determining the state behind the emerged shocks which originate at the interaction point. The location of these shocks in space time being unknown the problem constitutes a double free boundary problem, i.e.~complete data for the problem is only given in a single point, the interaction point. This article can be viewed as an extension of the article arXiv:2112.15266 which deals with the reflection of a shock on a wall.