Abstract
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 [8]. 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.
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