Acta mathematica scientia, Series B >
RELATIVE ENTROPY AND COMPRESSIBLE POTENTIAL FLOW
Received date: 2014-11-08
Online published: 2015-07-01
Supported by
This material is based upon work partially supported by the National Science Foundation under Grant No. NSF DMS-1054115 and by a Sloan Foundation Research Fellowship.
Compressible (full) potential flow is expressed as an equivalent first-order system of conservation laws for density 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 Dafer- mos/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 per- turbations 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.
Key words： potential flow; entropy; relative entropy; shock
Volker ELLING . RELATIVE ENTROPY AND COMPRESSIBLE POTENTIAL FLOW[J]. Acta mathematica scientia, Series B, 2015 , 35(4) : 763 -776 . DOI: 10.1016/S0252-9602(15)30020-5
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