Fokker–Planck Equations for SPDE with Non-trace-class Noise

Abstract

In this paper we develop a new technique to prove existence of solutions of Fokker–Planck equations on Hilbert spaces for Kolmogorov operators with non-trace-class second order coefficients or equivalently with an associated stochastic partial differential equation (SPDE) with non-trace-class noise. Applications include stochastic 2D and 3D-Navier–Stokes equations with non-trace-class additive noise.

Keywords

Fokker–Planck equation / Kolmogorov operator / Stochastic Partial Differential Equations / Stochastic Navier–Stokes equations / Non-trace-class noise

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