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Time regularity of the densities for the Navier--Stokes equations with noise

We prove that the density of the law of any finite dimensional projection of solutions of the Navier--Stokes equations with noise in dimension $3$ is Hölder continuous in time with values in the natural space $L^1$. When considered with values in Besov spaces, Hölder continuity still holds. The Hölder exponents correspond, up to arbitrarily small corrections, to the expected diffusive scaling.