Existence of a density of the 2Dim Stochastic Navier Stokes Equation driven by Levy processes or fractional Brownian motion

Abstract

In this article we are interested in the regularity properties of the probability measure induced by the solution process of the L\'evy noise or a fractional Brownian motion driven Navier Stokes Equation on the two dimensional torus $\mathbb{T}$. We mainly investigate under which conditions on the characteristic measure of the L\'evy process or the Hurst parameter of the fractal Brownian motion the law of the projection of $u(t)$ onto any finite dimensional $F\subset L^2(\mathbb{T})$ is absolutely continuous with respect to the Lebesgue measure on $F$.