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

2014/09/05 by Marco Romito, Romito, Marco · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · Physics and Astronomy · #35Q30 #60G30 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Primary 76M35 #Probability (math.PR) #Secondary 60H15 #Stochastic processes and financial applications #math-ph #math.AP #math.MP #math.PR #msc:35Q30 #msc:60G30 #msc:60H15 #msc:76M35

paper · pdf · doi:10.48550/arxiv.1409.1700

arxiv created 2014/09/05 · openalex publication_date 2014/09/05 · arxiv updated 2014/09/08 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

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 Hölder continuous in time with values in the natural space L¹. When considered with values in Besov spaces, Hölder continuity still holds. The Hölder exponents correspond, up to arbitrarily small corrections, to the expected diffusive scaling.

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