Rigorous results in space-periodic two-dimensional turbulence

Sergei Kuksin (1) , Armen Shirikyan (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We survey the recent advance in the rigorous qualitative theory of the 2d stochastic Navier-Stokes system that is relevant to the description of turbulence in two-dimensional fluids. After discussing briefly the initial-boundary value problem and the associated Markov process, we formulate results on the existence, uniqueness, and mixing of a stationary measure. We next turn to various consequences of these properties: strong law of large numbers, central limit theorem, and random attractors related to a unique stationary measure. We also discuss the Donsker-Varadhan and Freidlin-Wentzell type large deviations, the inviscid limit, and asymptotic results in 3d thin domains. We conclude with some open problems. Published by AIP Publishing. https://doi.

Domaines: Mathématiques [math]; Physique mathématique [math-ph]

Sergei Kuksin, Armen Shirikyan. Rigorous results in space-periodic two-dimensional turbulence. Physics of Fluids, 2017, 29 (12), pp.125106. ⟨10.1063/1.4996545⟩. ⟨hal-02385893⟩