The Euler equations of an inviscid incompressible fluid driven by a Lévy noise

Abstract

Our aim in this article is to show the local existence of pathwise solutions of the Euler equations driven by a general Lévy noise, in all space dimensions and for strictly positive time almost surely. The Euler equations are considered in a regular domain with slip boundary condition, or with periodic boundary conditions or in the whole space. In addition, we prove that when all data are $C^{\infty}$ in space, so is the solution.