Admissibility criteria for convex integration fan solutions and contact discontinuities in the Euler equation

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Original abstract

For a general piecewise constant fan subsolution to the isentropic Euler equations, the explicit computation of the entropy and action rates of any associated convex integration solution, relative to a common reference solution, shows that these rates depend only upon the fan. Moreover, these explicit expressions may be decomposed into a kinetic-energy mismatch and an internal-energy mismatch from which we characterize agreement of Dafermos' entropy rate criterion with action rate criteria. We apply this to the solutions constructed by Krupa and Székelyhidi for Riemann data whose classical solution is a planar contact discontinuity. Certified exact-arithmetic computations show that, in pairwise comparison, both criteria prefer the convex integration solutions to the classical self-similar solution.

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• Official / arXiv page
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