Nonunique admissible weak solutions of the compressible Euler equations with compact support in space

• Verfasst von: Akramov, Ibrokhimbek [VerfasserIn]
• Verfasst von: Wiedemann, Emil [VerfasserIn]
• Titel: Nonunique admissible weak solutions of the compressible Euler equations with compact support in space
• Verf.angabe: Ibrokhimbek Akramov and Emil Wiedemann
• E-Jahr: 2021
• Jahr: February 1, 2021
• Umfang: 18 S.
• Teil: volume:53
• Teil: year:2021
• Teil: number:1
• Teil: pages:795-812
• Teil: extent:18
• Fussnoten: Gesehen am 28.07..2021
• Titel Quelle: Enthalten in: Society for Industrial and Applied MathematicsSIAM journal on mathematical analysis
• Ort Quelle: Philadelphia, Pa. : SIAM, 1970
• Jahr Quelle: 2021
• Band/Heft Quelle: 53(2021), 1, Seite 795-812
• ISSN Quelle: 1095-7154
• DOI: doi:10.1137/20M1367015
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1754738370

Abstract

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.