Rigorous results in space-periodic two-dimensional turbulence

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.
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Contributeur : Armen Shirikyan <>
Soumis le : jeudi 28 décembre 2017 - 16:18:17
Dernière modification le : jeudi 3 mai 2018 - 15:18:02

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Sergei Kuksin, Armen Shirikyan. Rigorous results in space-periodic two-dimensional turbulence. Physics of Fluids, American Institute of Physics, 2017, 29, pp.125106. 〈http://aip.scitation.org/doi/10.1063/1.4996545〉. 〈hal-01673113〉

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