Fokker-Planck equations for SPDE with non-trace class noise

TL;DR

This paper introduces a novel method to establish the existence of solutions for Fokker-Planck equations related to SPDEs driven by non trace-class noise, with applications to complex fluid dynamics models.

Contribution

It develops a new technique to prove existence of solutions for Fokker-Planck equations with non trace-class noise, extending analysis to challenging SPDEs.

Findings

Proved existence of solutions for Fokker-Planck equations with non trace-class coefficients.

Applied the method to stochastic 2D and 3D Navier-Stokes equations.

Extended the theoretical framework for SPDEs 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.