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 H\"older continuous, thus improving the results of Debussche and Romito
[DebRom2014].
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
