Abstract
In this paper, we rigorously prove the existence of self-similar converging shock wave solutions for the non-isentropic Euler equations for γ ∈ (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.
| Original language | English |
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| Journal | Archive for Rational Mechanics and Analysis |
| Publication status | Acceptance date - 11 Feb 2025 |
Acknowledgements
JJ and JL are supported in part by the NSF grants DMS-2009458 and DMS-2306910. MS is supported by the EPSRC Post-doctoral Research Fellowship EP/W001888/1. The authors would also like to thank the anonymous reviewer for their generous comments and advice, which has improved the presentation of the paper.Funding
Engineering and Physical Sciences Research Council - EP/W001888/1 National Science Foundation - DMS-2009458, DMS-2306910
| Funders | Funder number |
|---|---|
| Engineering and Physical Sciences Research Council |
