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

2015/07/09 by Marco Romito, Romito, Marco · 1 citation
Mathematics · #35Q30 #60G30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 76M35 #Probability (math.PR) #Secondary 60H15 #math.AP #math.PR #msc:35Q30 #msc:60G30 #msc:60H15 #msc:76M35

paper · pdf · doi:10.48550/arxiv.1507.02742

arxiv created 2015/07/09 · arxiv updated 2015/07/13

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 Hölder 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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