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 language||English (US)|
|Number of pages||19|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Sep 2004|
ASJC Scopus subject areas
- Applied Mathematics