On admissibility criteria for weak solutions of the Euler equations

Details On admissibility criteria for weak solutions of the Euler equations On admissibility criteria for weak solutions of the Euler equations

2007-12-19

arxiv.org/abs/0712.3288v2

Arch. Ration. Mech. Anal. 195 (2010), no. 1, 225-260

Mathematics

Analysis of PDEs

33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proofs

Scientific paper

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.

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