Convergence of the stochastic Navier-Stokes-$\alpha$ solutions toward the stochastic Navier-Stokes solutions

Jad Doghman; Ludovic Goudenège

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arXiv · 2210.02232

Convergence of the stochastic Navier-Stokes-$\alpha$ solutions toward the stochastic Navier-Stokes solutions

Jad Doghman·Ludovic Goudenège

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Abstract

Loosely speaking, the Navier-Stokes-$\alpha$ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted $\alpha$. Starting from a strong two-dimensional solution to the Navier-Stokes-$\alpha$ model driven by a multiplicative noise, we demonstrate that it generates a strong solution to the stochastic Navier-Stokes equations under the condition $\alpha$ 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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Jad Doghman, Ludovic Goudenège. 2022-10-05. Convergence of the stochastic Navier-Stokes-$\alpha$ solutions toward the stochastic Navier-Stokes solutions. https://arxiv.org/abs/2210.02232

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