Exponential Convergence for the Stochastically Forced Navier-Stokes Equations and Other Partially Dissipative Dynamics

By Jonathan C. Mattingly. 2002

183 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a99295adea95c8dbd836922af793228c76910354

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Citations in the corpus

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].”
Couplings and quantitative contraction rates for Langevin dynamics (2017, methodology): “ respectively. Our approach is also related to the application of the strategy described above to innite-dimensional stochastic dierential equations with possibly degenerate noise in [48], cf. also [24, 34]. Besides providing an intuitive understanding for the mechanism of convergence to equilibrium”
Exponential ergodicity for stochastic Burgers and 2D Navier–Stokes equations (2005, methodology): “In all those papers various versions of coupling technique were applied to prove the convergence properties in metrics equivalent to the topology of weak convergence of measures (or an intermediate metric, cf. [ 26 ]).”
Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations (2006, methodology): “In particular, [20, 37, 38] developed a coupling construction to prove exponential convergence.”
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], [15], [17], [18], [19], [20], [21], [11], [22], [23]) when f(t) = 0.”
Ergodic BSDEs under weak dissipative assumptions (2010, background): “Our proof is a mix of arguments found in [7], [15], [16], [22] and [18].”
On ergodicity of some Markov processes (2008, methodology): “r a stochastic evolution equation is based on the strong Feller property of the transition semigroup (see [3, 6, 10] and [22]) or, in a more reﬁned form, on the asymptotic strong Feller property (see [11, 12, 19]). In our Theorem 3, we do not require either of these properties of the corresponding s”
Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes (2016, background): “The key idea was to replace the underlying couplings with finite coupling time by asymptotic couplings where the coupled processes only approach each other as t → ∞ [26,44] and the minorization condition by a contraction in an appropriately chosen Kantorovich distance.”
Generalized couplings and ergodic rates for SPDEs and other Markov models (2018, methodology): “Note that exponential ergodic bounds had been obtained previously for the Navier-Stokes equation only on a 2-dimensional torus, see [31] and [21].”
Ergodicity of stochastic differential equations driven by fractional Brownian motion (2003, methodology): “The main tool used in the proof of Theorems 1.2 and 1.3 is a coupling construction similar in spirit to the ones presented in [ Mat02 , Hai02].”
Stochastic tamed 3D Navier–Stokes equations: existence, uniqueness and ergodicity (2008, methodology): “istence and pathwise uniqueness of L2-continuous adapted solutions. On the other hand, the ergodicity of invariant measures for 2D stochastic Navier-Stokes equations has been studied extensively (cf. [11, 22, 7, 15] and reference therein). Especially, Hairer and Mattingly [15] recently developed two”
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].”
Stabilization by noise for a class of stochastic reaction-diffusion equations (2005, unknown): “Concerning the coupling method, we recall that it has been used also recently by several other authors (see [11], [16] and [13] and references quoted therein),”
Strong and weak orders in averaging for SPDEs (2012, methodology): “This technique was first used in the study of the asymptotic behaviour of Markov chains – see [1,8,14,17] – and was later adapted for SDEs and more recently for SPDEs—see for instance [13,16].”
Ergodicity Results for the Stochastic Navier–Stokes Equations: An Introduction (2013, methodology): “Then, another essential progress was obtained in [49] where coupling argument were used and exponential convergence to equilibrium was obtained again under the assumption that sufficiently many modes are forced.”