@article { ISI:000426146600005, title = {A large deviations principle for stochastic flows of viscous fluids}, journal = {JOURNAL OF DIFFERENTIAL EQUATIONS}, volume = {264}, number = {{8}}, year = {2018}, note = {

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}, month = {{APR 15}}, pages = {5070-5108}, publisher = {{ACADEMIC PRESS INC ELSEVIER SCIENCE}}, type = {{Article}}, address = {{525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA}}, abstract = {

{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.}

}, keywords = {Euler equations, Lagrangian flows, Large deviations principle}, Stochastic differential equations, Stochastic flows, {Navier-Stokes equations}, issn = {{0022-0396}}, doi = {{10.1016/j.jde.2017.12.031}}, author = {Cipriano, Fernanda and Costa, Tiago} }