Gibbsian Dynamics and Ergodicity¶for the Stochastically Forced Navier–Stokes Equation

By W. E, J. Mattingly, Y. Sinai. 2001

249 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/62d5a2c60948dea917a581f90909d0977953188f

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Citations in the corpus

Ergodic Theory of Infinite Dimensional Systems¶with Applications to Dissipative Parabolic PDEs (2002, methodology): “Ergodic Theory of Infinite Dimensional Systems with Applications to Dissipative Parabolic PDEs Nader Masmoudi1 and Lai-Sang Young2 Courant Institute of Mathematical Sciences 251 Mercer Street, New York, NY 10012 May 12, 2001”
Ergodicity for the Navier‐Stokes equation with degenerate random forcing: Finite‐dimensional approximation (2001, unknown): “In fact, for the full Navier-Stokes equation, the only existing result so far for the uniqueness of an invariant measure under degenerate noise is for the case when all determining modes are forced [2, 4, 14].”
2D Stochastic Navier–Stokes Equations with a Time-Periodic Forcing Term (2008, background): “Recently much progress has been obtained in the study of existence, uniqueness and ergodicity of the associated invariant measures [3,11,15,17–23] when f (t)= 0.”
Hypocoercivity (2006, unknown): “Some of these studies were motivated by the study of finite-dimensional approximations of randomly forced two-dimensional Navier-Stokes equations [17, 36, 35]; since then, the theory has been developed to the extent that it can deal with truly infinite-dimensional systems [28].”
A Theory of Hypoellipticity and Unique Ergodicity for Semilinear Stochastic PDEs (2008, methodology): “tesimal” version of techniques developed in [EMS0 1, KS00] and extended in [BKL01, MY02, Mat02, Hai02, BM05] combined with detailed lower bounds on the Malliavin covariance matrix of the solution. In [EMS01] the idea was the following: take two distinct initial conditions u0 and u′ 0 for (1.1) and a”
Exponential ergodicity for stochastic Burgers and 2D Navier–Stokes equations (2005, background): “The exponential rate of convergence of transition measures to the invariant measure μ of the stochastic Navier-Stokes equation was proved for the first time in [1] for μ-almost every initial condition and subsequently for every square integrable initial condition in [22] and [26] (see also [10]).”