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Relative entropy and compressible potential flow

ELLING, Volker

Acta mathematica scientia: Shu xue wu li xue bao. Volume 35:Issue 4 (2015, April); pp 763-776 -- Elsevier Ltd

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  • Title:
    Relative entropy and compressible potential flow
  • Author: ELLING, Volker
  • Found In: Acta mathematica scientia: Shu xue wu li xue bao. Volume 35:Issue 4 (2015, April); pp 763-776
  • Journal Title: Acta mathematica scientia: Shu xue wu li xue bao
  • Subjects: Mathematical physics--Periodicals; Dewey: 530.15
  • Rights: legaldeposit
  • Publication Details: Elsevier Ltd
  • Abstract: Abstract

    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 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.


  • Identifier: ETOClsidyv960c5fb6; System Number: LDEAvdc_100025922707.0x000001; Journal ISSN: 0252-9602; 10.1016/S0252-9602(15)30020-5
  • Publication Date: 2015
  • Physical Description: Electronic
  • Shelfmark(s): ELD Digital store

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