Eddy viscosity by Lévy transport noises

Abstract

We consider stochastic 2D Euler equations with $L^2$-initial vorticity and driven by Lévy transport noise in the Marcus sense. Under a suitable scaling limit of the noises, we prove that the weak solutions converge weakly to the unique solution of the deterministic 2D Navier-Stokes equation. This shows that small scale jump noises generate eddy viscosity, extending the recent studies on Itô-Stratonovich diffusion limit to discontinuous setting.

41 pages