Large deviations for stochastic tamed 3D Navier-Stokes equations
type: Item
instance of: scholarly article
title: Large deviations for stochastic tamed 3D Navier-Stokes equations
zbMATH Open document ID: 1195.60093
author: Xicheng Zhang
author: Michael Röckner
author: Tu-Sheng Zhang
published in: Applied Mathematics and Optimization
publication date: 2010-04-20T00:00:00Z
review text: The paper deals with the stochastic tamed 3 dimensional Navier-Stokes equation driven by multiplicative Gaussian noise. They consider the equation on the hole Euclidian space or on the torus and prove a small noise large deviation of Freidlin-Wentzell type. The main ingredient of the proof is the weak convergence approach by Dupuis-Ellis. They rewrite the equation to an abstract stochastic evolution one and prove that the perturbed evolution equation satisfies the large deviation principle. Existence and uniqueness results are dealt with in a former paper of the authors.
reviewed by: Michael Stauch
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 5695470
zbMATH Keywords: large deviation
zbMATH Keywords: stochastic tamed 3D Navier-Stokes equation
zbMATH Keywords: weak convergence method
MaRDI profile type: Publication
full work available at URL: s00245-009-9089-6
OpenAlex ID: W2102548863
cites work: Elliptic equations for measures on infinite dimensional spaces and applications
cites work: A variational representation for certain functionals of Brownian motion
cites work: A variational representation for positive functionals of infinite dimensional Brownian motion
cites work: Large deviations for infinite dimensional stochastic dynamical systems
cites work: Uniform large deviations for parabolic SPDEs and applications
cites work: Large deviations for a Burgers'-type SPDE
cites work: Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term.
cites work: Ergodicity for the 3D stochastic Navier-Stokes equations
cites work: Markov solutions for the 3D stochastic Navier-Stokes equations with state dependent noise
cites work: Q4391441
cites work: Q4388221
cites work: Markov selections for the 3D stochastic Navier-Stokes equations
cites work: Martingale solutions and Markov selections for stochastic partial differential equations
cites work: Large deviations for stochastic evolution equations with small multiplicative noise
cites work: Stochastic Navier--Stokes Equations for Turbulent Flows
cites work: A concise course on stochastic partial differential equations
cites work: Freidlin-Wentzell's large deviations for homeomorphism flows of non-Lipschitz SDEs
cites work: Freidlin-Wentzell's large deviations for stochastic evolution equations
cites work: Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity
cites work: TAMED 3D NAVIER–STOKES EQUATION: EXISTENCE, UNIQUENESS AND REGULARITY
cites work: Large deviations for a reaction-diffusion equation with non-Gaussian perturbations
cites work: On the small time asymptotics of diffusion processes on Hilbert spaces.
cites work: Euler schemes and large deviations for stochastic Volterra equations with singular kernels
cites work: Stochastic Volterra equations in Banach spaces and stochastic partial differential equation
cites work: A variational representation for random functionals on abstract Wiener spaces
DOI: 10.1007/S00245-009-9089-6
description: scientific article; zbMATH DE number 5695470