The incompressible limit of solutions of the two‐dimensional compressible Euler system with degenerating initial data

Using Strichartz estimates, it is possible to pass to the limit in the weakly compressible 2‐D Euler system, when the Mach number ? tends to zero, even if the initial data are not uniformly smooth. More precisely, their norms in Sobolev spaces embedded in C¹ can be allowed to grow as small powers of ?^?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.