We prove that the density of the law of any finite dimensional projection of solutions of the Navier--Stokes equations with noise in dimension 3 is Holder continuous in time with values in the natural space L^1. When considered with values in Besov spaces, Holder continuity still holds. The Holder exponents correspond, up to arbitrarily small corrections, to the expected, at least with the known regularity, diffusive scaling.
Time regularity of the densities for the Navier-Stokes equations with noise
ROMITO, MARCO
2016-01-01
Abstract
We prove that the density of the law of any finite dimensional projection of solutions of the Navier--Stokes equations with noise in dimension 3 is Holder continuous in time with values in the natural space L^1. When considered with values in Besov spaces, Holder continuity still holds. The Holder exponents correspond, up to arbitrarily small corrections, to the expected, at least with the known regularity, diffusive scaling.File in questo prodotto:
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