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.
Hölder regularity of the densities for the Navier-Stokes equations with noise
ROMITO, MARCO
2016-01-01
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 (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.File in questo prodotto:
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