Nonunique admissible weak solutions of the compressible Euler equations with compact support in space
This paper is concerned with the existence of compactly supported admissible solutions to the Cauchy problem for the isentropic compressible Euler equations. In more than one space dimension, convex integration techniques developed by De Lellis and Székelyhidi and by Chiodaroli enable us to prove f...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
February 1, 2021
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| In: |
SIAM journal on mathematical analysis
Year: 2021, Jahrgang: 53, Heft: 1, Pages: 795-812 |
| ISSN: | 1095-7154 |
| DOI: | 10.1137/20M1367015 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/20M1367015 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/20M1367015 
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| Verfasserangaben: | Ibrokhimbek Akramov and Emil Wiedemann |
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| 520 | |a This paper is concerned with the existence of compactly supported admissible solutions to the Cauchy problem for the isentropic compressible Euler equations. In more than one space dimension, convex integration techniques developed by De Lellis and Székelyhidi and by Chiodaroli enable us to prove failure of uniqueness on a finite time-interval for admissible solutions starting from any continuously differentiable initial density and suitably constructed bounded initial momenta. In particular, this extends Chiodaroli's work from periodic boundary conditions to bounded domains or the whole space. | ||
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