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 |
|---|---|
| Article number | 24 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 249 |
| Issue number | 3 |
| Early online date | 3 Apr 2025 |
| DOIs | |
| Publication status | Published - 30 Jun 2025 |
Data Availability Statement
All data generated or analysed during this study is included in this published article.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
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.
| Funders | Funder number |
|---|---|
| Neurosciences Foundation | DMS-2009458, DMS-2306910 |
| Engineering and Physical Sciences Research Council | EP/W001888/1 |
