Inviscid Large deviation principle and the 2D Navier Stokes equations with a free boundary condition

Hakima Bessaih (1) , Annie Millet (2, 3)

1 Department of Mathematics, University of Wyoming
2 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root of the viscosity. Unlike previous results on LDP for hydrodynamical models, the weak convergence is proven by tightness properties of the distribution of the solution in appropriate functional spaces.

Mots clés: Models of turbulence; viscosity coefficient and Navier-Stokes equations; Euler equation; stochastic PDEs; Radonifying operators; large deviations

Domaines: Probabilités [math.PR]

Hakima Bessaih, Annie Millet. Inviscid Large deviation principle and the 2D Navier Stokes equations with a free boundary condition. 2010. ⟨hal-00537662v1⟩