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The incompressible limit of solutions of the two‐dimensional compressible Euler system with degenerating initial data
Author(s) -
Dutrifoy Alexandre,
Hmidi Taoufik
Publication year - 2004
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20026
Subject(s) - euler system , mathematics , compressibility , limit (mathematics) , euler equations , sobolev space , zero (linguistics) , mathematical analysis , mach number , euler's formula , convergence (economics) , compressible flow , backward euler method , vortex , physics , mechanics , linguistics , philosophy , economics , economic growth
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 zero, 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. © 2000 Wiley Periodicals, Inc.