On the 2D Isentropic Euler System with Unbounded Initial vorticity

Zineb Hassainia (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Keywords: 2D compressible Euler equations; Incompressible limit; {\rm BMO}-type spaces

Domains: Analysis of PDEs [math.AP]

Zineb Hassainia. On the 2D Isentropic Euler System with Unbounded Initial vorticity. Journal of Differential Equations, 2015, 259 (1), pp.264-317. ⟨10.1016/j.jde.2015.02.008⟩. ⟨hal-00874419⟩