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arXiv · 1507.02742

H\"older regularity of the densities for the Navier--Stokes equations with noise

Marco Romito
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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 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.

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Marco Romito. 2015-07-09. H\"older regularity of the densities for the Navier--Stokes equations with noise. https://arxiv.org/abs/1507.02742

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