Work

Convergence of the Stochastic Navier–Stokes-$$\alpha $$ Solutions Toward the Stochastic Navier–Stokes Solutions

Year: 2025

Type: article

Abstract: Loosely speaking, the Navier–Stokes- $$\alpha $$ α model and the Navier–Stokes equations differ by a spatial filtration parametrized by a scale denoted $$\alpha $$ α . Starting from a strong two-dimensional solution to the Navier–Stokes- $$\alpha $$ α model driven by a multiplicative noise, we demonstrate that it generates a strong solution to the stochastic Navier–Stokes equations under the condition $$\alpha \rightarrow 0$$ α → 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.

Source: Applied Mathematics & Optimization

DOI: 10.1007/s00245-025-10228-8

Authors: Jad Doghman, Ludovic Goudenège

Institutions: Centre National de la Recherche Scientifique, Université Paris-Saclay, CentraleSupélec

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,890

Funders: Agence Nationale de la Recherche, Fondation Mathématique Jacques Hadamard