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Preprints, Working Papers, ... Year : 2022

Convergence of the stochastic Navier-Stokes-α solutions toward the stochastic Navier-Stokes solutions

Abstract

Loosely speaking, the Navier-Stokes-⍺ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted ⍺. Starting from a strong two-dimensional solution to the Navier-Stokes-α model driven by a multiplicative noise, we demonstrate that it generates a strong solution to the stochastic Navier-Stokes equations under the condition ⍺ goes to 0. The initially introduced probability space and the Wiener process are maintained throughout the investigation, thanks to a local monotonicity property that abolishes the use of Skorokhod’s theorem. High spatial regularity a priori estimates for the fluid velocity vector field are carried out within periodic boundary conditions.
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Dates and versions

hal-03794814 , version 1 (03-10-2022)

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Jad Doghman, Ludovic Goudenège. Convergence of the stochastic Navier-Stokes-α solutions toward the stochastic Navier-Stokes solutions. 2022. ⟨hal-03794814⟩
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