The incompressible limit of solutions of the two-dimensional compressible euler system with degenerating initial data

Alexandre Dutrifoy, Taoufik Hmidi

Research output: Contribution to journalArticlepeer-review

Abstract

Using Strichartz estimates, it is possible to pass to the limit in the weakly compressible 2-D Euler system when the Mach number ε tends to 0, even if the initial data are not uniformly smooth. More precisely, their norms in Sobolev spaces embedded in C 1 can be allowed to grow as small powers of ε -1. This leads to results of convergence to solutions of the incompressible Euler system whose regularity is critical, such as vortex patches or Yudovich solutions.

Original languageEnglish (US)
Pages (from-to)1159-1177
Number of pages19
JournalCommunications on Pure and Applied Mathematics
Volume57
Issue number9
DOIs
StatePublished - Sep 2004

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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