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

Akramov I, Wiedemann E (2021)

Publication Type: Journal article

Publication year: 2021

Journal

SIAM Journal on Mathematical Analysis Society for Industrial and Applied Mathematics

Book Volume: 53

Pages Range: 795-812

Journal Issue: 1

DOI: 10.1137/20M1367015

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.

Authors with CRIS profile

Emil Wiedemann

Involved external institutions

Ruprecht-Karls-Universität Heidelberg DE Germany (DE) Universität Ulm DE Germany (DE)

How to cite

APA:

Akramov, I., & Wiedemann, E. (2021). Nonunique admissible weak solutions of the compressible Euler equations with compact support in space. SIAM Journal on Mathematical Analysis, 53(1), 795-812. https://dx.doi.org/10.1137/20M1367015

MLA:

Akramov, Ibrokhimbek, and Emil Wiedemann. "Nonunique admissible weak solutions of the compressible Euler equations with compact support in space." SIAM Journal on Mathematical Analysis 53.1 (2021): 795-812.

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