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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.

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