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arXiv · 2310.18483

On self-similar converging shock waves

Juhi Jang·Jiaqi Liu·Matthew Schrecker
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Abstract

In this paper, we rigorously prove the existence of self-similar converging shock wave solutions for the non-isentropic Euler equations for $γ\in (1,3]$. These solutions are analytic away from the shock interface before collapse, and the shock wave reaches the origin at the time of collapse. The region behind the shock undergoes a sonic degeneracy, which causes numerous difficulties for smoothness of the flow and the analytic construction of the solution. The proof is based on continuity arguments, nonlinear invariances, and barrier functions.

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Juhi Jang, Jiaqi Liu, Matthew Schrecker. 2023-10-27. On self-similar converging shock waves. https://arxiv.org/abs/2310.18483

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