On the 2D Isentropic Euler System with Unbounded Initial vorticity

This paper is devoted to the study of the low Mach number limit for the 2D isentropic Euler system associated to ill-prepared initial data with slow blow up rate on $\log\varepsilon^{-1}$. We prove in particular the strong convergence to the solution of the incompressible Euler system when the vorticity belongs to some weighted $BMO$ spaces allowing unbounded functions. The proof is based on the extension of the result of \cite{B-K} to a compressible transport model.