Convergence of the Stochastic Navier–Stokes-α Solutions Toward the Stochastic Navier–Stokes Solutions

• Published in: Applied mathematics & optimization Vol. 91; no. 2; p. 32
• Main Authors: Doghman, Jad, Goudenège, Ludovic
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2025; Springer Nature B.V; Springer Verlag (Germany)
• Subjects: Analysis of PDEs; Applied mathematics; Approximation; Boundary conditions; Calculus of Variations and Optimal Control; Optimization; Control; Fields (mathematics); Fluid flow; Fluid mechanics; Investigations; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Mechanics; Navier-Stokes equations; Noise generation; Numerical and Computational Physics; Optimization; Physics; Probability; Simulation; Systems Theory; Theoretical; Velocity; 37L55; Multiplicative noise; Cylindrical Wiener process; 60H30; 35Q35; Navier–Stokes; 76D05; 35Q30; 60H15; Strong solutions; Navier-Stokes; Multiplicative noises; Navier-Stokes-α
• ISSN: 0095-4616; 1432-0606
• DOI: 10.1007/s00245-025-10228-8

Loosely speaking, the Navier–Stokes- α model and the Navier–Stokes equations differ by a spatial filtration parametrized by a scale denoted α . 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 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.