Time regularity of the densities for the Navier-Stokes equations with noise.

*(English)*Zbl 1360.76218Summary: 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.

##### MSC:

76M35 | Stochastic analysis applied to problems in fluid mechanics |

60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |

60G30 | Continuity and singularity of induced measures |

35Q30 | Navier-Stokes equations |

##### Keywords:

density of laws; Navier-Stokes equations; stochastic partial differential equations; Besov spaces; Girsanov transformation; time regularity of densities##### References:

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