Non-Unique 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-Székelyhidi and Chiodaroli enable us to prove failure o...

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Bibliographic Details
Published in:arXiv.org 2020-03
Main Authors: Akramov, Ibrokhimbek, Wiedemann, Emil
Format: Article
Language:English
Subjects:
Boundary conditions
Cauchy problems
Compressibility
Euler-Lagrange equation
Eulers equations
Mathematical analysis
Online Access:Get full text
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Summary: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-Székelyhidi and 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.
ISSN:2331-8422