Coupling approach to white-forced nonlinear PDEs

By Sergei B. Kuksin, Armen Shirikyan. 2002

102 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/dad31e5bb030b93190ca9b98da54e9fd37fb060f

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Citations in the corpus

Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations (2006, result): “We should also remark that previous estimates, such as [20, 29, 37, 38], giving simply exponential convergence to equilibrium are weaker and the results in this article represent a significant and new extension of those results.”
Asymptotic coupling and a general form of Harris’ theorem with applications to stochastic delay equations (2009, background): “While even simple, formally elliptic, linear SPDEs can have transition probabilities which are mutually singular, the bulk of recent work has been motivated by equations driven by noise which is “degenerate” to varying degrees [EH01, BKL01, EMS01, KS02 , Mat02b, HM06, HM08a].”
Exponential mixing for stochastic PDEs: the non-additive case (2005, methodology): “These arguments have initially been used in the context of dissipative SPDEs in [23], [26].”
Exponential ergodicity and regularity for equations with Lévy noise (2011, background): “We refer the reader to [13,19,35] for discrete-time random perturbations, to [21,11,14,36,24] for a white noise, to [22] for a compound Poisson process, and to the book [15] for further references on this subject.”
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]).”
Ergodicity Results for the Stochastic Navier–Stokes Equations: An Introduction (2013, methodology): “Then, these arguments were generalized in several directions and the theory was extended to many other equations (see for instance [23], [35], [37], [43], [41], [44], [45] , [46], [56], [57], [63]).”