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 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.