A general convex integration scheme for the isentropic compressible Euler equations

Dȩbiec T, Skipper J, Wiedemann E (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Journal of Hyperbolic Differential Equations World Scientific Publishing

Book Volume: 20

Pages Range: 95-117

Journal Issue: 1

DOI: 10.1142/S0219891623500042

Abstract

We prove via convex integration a result that allows to pass from a so-called subsolution of the isentropic Euler equations (in space dimension at least 2) to exact weak solutions. The method is closely related to the incompressible scheme established by De Lellis-Székelyhidi, in particular, we only perturb momenta and not densities. Surprisingly, though, this turns out not to be a restriction, as can be seen from our simple characterization of the Λ -convex hull of the constitutive set. An important application of our scheme has been exhibited in recent work by Gallenmüller-Wiedemann.

Authors with CRIS profile

Emil Wiedemann Lehrstuhl für Analysis

Involved external institutions

University of Warsaw / Uniwersytet Warszawski PL Poland (PL) Universität Ulm DE Germany (DE)

How to cite

APA:

Dȩbiec, T., Skipper, J., & Wiedemann, E. (2023). A general convex integration scheme for the isentropic compressible Euler equations. Journal of Hyperbolic Differential Equations, 20(1), 95-117. https://dx.doi.org/10.1142/S0219891623500042

MLA:

Dȩbiec, Tomasz, Jack Skipper, and Emil Wiedemann. "A general convex integration scheme for the isentropic compressible Euler equations." Journal of Hyperbolic Differential Equations 20.1 (2023): 95-117.

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