Characterization of the law for 3D stochastic hyperviscous fluids

Abstract

We consider the 3D hyperviscous Navier-Stokes equations in vorticity form, where the dissipative term $-\Delta \vec \xi $ of the Navier-Stokes equations is substituted by $(-\Delta )^{1+c} \vec \xi $. We investigate how big the correction term $c$ has to be in order to prove, by means of Girsanov transform, that the vorticity equations are equivalent (in law) to easier reference equations obtained by neglecting the stretching term. This holds as soon as $c>\frac 12$, improving previous results obtained with $c>\frac 32$ in a different setting in [5, 14].