Stochastic vorticity equation in ${\mathbb{R}}^2$ with not regular noise

Abstract

We consider the Navier-Stokes equations in vorticity form in ${\mathbb{R}}^2$ with a white noise forcing term of multiplicative type, whose spatial covariance is not regular enough to apply the Itô calculus in $L^q$ spaces, $1<q<\infty$. We prove the existence of a unique strong (in the probability sense) solution.