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arXiv · 1411.2063

Relative entropy and compressible potential flow

Volker Elling
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Abstract

Compressible (full) potential flow is expressed as an equivalent first-order system of conservation laws for density $ρ$ and velocity $v$. Energy $E$ is shown to be the only nontrivial entropy for that system in multiple space dimensions, and it is strictly convex in $ρ,v$ if and only if $|v|<c$. For motivation some simple variations on the relative entropy theme of Dafermos/DiPerna are given, for example that smooth regions of weak entropy solutions shrink at finite speed, and that smooth solutions force solutions of singular entropy-compatible perturbations to converge to them. We conjecture that entropy weak solutions of compressible potential flow are unique, in contrast to the known counterexamples for the Euler equations.

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Volker Elling. 2015-04-06. Relative entropy and compressible potential flow. https://arxiv.org/abs/1411.2063

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