%0 Journal Article %J JOURNAL OF DIFFERENTIAL EQUATIONS %D 2018 %T A large deviations principle for stochastic flows of viscous fluids %A Cipriano, Fernanda %A Costa, Tiago %C {525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA} %I {ACADEMIC PRESS INC ELSEVIER SCIENCE} %K Euler equations %K Lagrangian flows %K Large deviations principle} %K Stochastic differential equations %K Stochastic flows %K {Navier-Stokes equations %P 5070-5108 %R {10.1016/j.jde.2017.12.031} %V 264 %X

{We study the well-posedness of a stochastic differential equation on the two dimensional torus T-2, driven by an infinite dimensional Wiener process with drift in the Sobolev space L-2 (0, T; H-1 (T-2)). The solution corresponds to a stochastic Lagrangian flow in the sense of DiPerna Lions. By taking into account that the motion of a viscous incompressible fluid on the torus can be described through a suitable stochastic differential equation of the previous type, we study the inviscid limit. By establishing a large deviations principle, we show that, as the viscosity goes to zero, the Lagrangian stochastic Navier-Stokesflow approaches the Euler deterministic Lagrangian flow with an exponential rate function. (c) 2018 Elsevier Inc. All rights reserved.}

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%8 {APR 15} %9 {Article}