Homogenization of the 2d Euler system in porous media

In this talk I will discuss some homogenization results for the 2D Euler system with impermeable inclusions. The main difficulty is the homogenization of the transport equation for the vorticity. Localization for the latter could indeed rule out separation of scales. To prevent this and establish homogenization towards a variant of the Euler system, we combine classical results from different areas : homogenization of elliptic systems with stiff inclusions, unique ergodicity for dynamical systems, complex analysis à la Rado-Kneser-Choquet, and large-scale regularity. I will conclude with some open problems on invariant measures in the random case. This is joint work with Mitia Duerinckx (ULB).