Mixing via controllability for randomly forced nonlinear dissipative PDEs

DOI10.5802/jep.130zbMath1451.35071arXiv1902.00494OpenAlexW2914766253WikidataQ114013366 ScholiaQ114013366MaRDI QIDQ2208626

Vahagn Nersesyan, Armen R. Shirikyan, Sergej B. Kuksin

Publication date: 3 November 2020

Published in: Journal de l'École Polytechnique -- Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.00494

zbMATH Keywords

Lyapunov functionMarkov processstationary measureHaar series

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Control/observation systems governed by partial differential equations (93C20) Stochastic analysis applied to problems in fluid mechanics (76M35) Ergodicity, mixing, rates of mixing (37A25) Linearizations (93B18) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Infinite-dimensional random dynamical systems; stochastic equations (37L55) Semilinear parabolic equations (35K58)

Related Items (8)

Ergodicity for the randomly forced Navier-Stokes system in a two-dimensional unbounded domain ⋮ Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes ⋮ Quantitative spectral gaps for hypoelliptic stochastic differential equations with small noise ⋮ Large deviations principle via Malliavin calculus for the Navier-Stokes system driven by a degenerate white-in-time noise ⋮ Controllability and ergodicity of three dimensional primitive equations driven by a finite-dimensional force ⋮ Approximate controllability of nonlinear parabolic PDEs in arbitrary space dimension ⋮ Exponential mixing for a class of dissipative PDEs with bounded degenerate noise ⋮ A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations

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