Rigorous results in space-periodic two-dimensional turbulence
Mathematical Physics
2017-12-29 v1 Analysis of PDEs
math.MP
Probability
Fluid Dynamics
Abstract
We survey the recent advance in the rigorous qualitative theory of the 2d stochastic Navier-Stokes system that are 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, as well as the inviscid limit and asymptotic results in 3d thin domains. We conclude with some open problems.
Cite
@article{arxiv.1712.09830,
title = {Rigorous results in space-periodic two-dimensional turbulence},
author = {Sergei Kuksin and Armen Shirikyan},
journal= {arXiv preprint arXiv:1712.09830},
year = {2017}
}