Fokker–Planck equations in Hilbert spaces

Abstract

This paper includes in an unified way several results about existence and uniqueness of solutions of Fokker–Planck equations from (Bogachev et al., J Funct Anal, 256:1269–1298, 2009) [2], (Bogachev et al., J Evol Equ, 10(3):487–509, 2010) [3], (Bogachev et al., Partial Differ Equ, 36:925–939, 2011) [4] and (Bogachev et al., Bull London Math Soc 39:631–640, 2007) [1], using probabilistic methods. Several applications are provided including Burgers and 2D-Navier–Stokes equations perturbed by noise. Some of these applications were also studied by a different analytic approach in (Bogachev et al., J Differ Equ, 259(8):3854–3873, 2015) [5], (Bogachev et al., Ann Sc Norm Super Pisa Cl Sci 14(3):983–1023, 2015) [6], (Da Prato et al., Commun Math Stat, 1(3):281–304, 2013) [11].