A General Convex Integration Scheme for the Isentropic Compressible Euler Equations

2021/07/22 by Dębiec, Tomasz, Skipper, Jack W. D., Wiedemann, Emil
#35Q31 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.10618

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 will be exhibited in forthcoming work by Gallenmüller--Wiedemann.

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