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

We prove that the densities of the finite dimensional projections of weak solutions of the Navier--Stokes equations driven by Gaussian noise are bounded and Holder continuous, thus improving the results of Debussche and Romito (2014). The proof is based on analytical estimates on a conditioned Fokker--Planck equation solved by the density, that has a ``non--local'' term that takes into account the influence of the rest of the infinite dimensional dynamics over the finite subspace under observation.