RELATIVE ENTROPY AND COMPRESSIBLE POTENTIAL FLOW

doi:10.1016/S0252-9602(15)30020-5

摘要/Abstract

摘要：

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.

关键词: potential flow, entropy, relative entropy, shock

Abstract:

Key words: potential flow, entropy, relative entropy, shock

中图分类号:

35L67

Volker ELLING. RELATIVE ENTROPY AND COMPRESSIBLE POTENTIAL FLOW[J]. 数学物理学报(英文版), 2015, 35(4): 763-776.

Volker ELLING. RELATIVE ENTROPY AND COMPRESSIBLE POTENTIAL FLOW[J]. Acta mathematica scientia,Series B, 2015, 35(4): 763-776.

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