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We prove that the density of the law of any finite-dimensional projection of solutions of the Navier–Stokes equations with noise in dimension three is Hölder continuous in time with values in the natural space L 1. When considered with values in Besov spaces, Hölder continuity still holds. The Hölder exponents correspond, up to arbitrarily small corrections, to the expected, at least with the known regularity, diffusive scaling.
Journal of Evolution Equations – Springer Journals
Published: Jan 5, 2016
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