A large deviations principle for stochastic flows of viscous fluids

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Cipriano, Fernanda^1,2  Costa, Tiago¹ 

[1] FCT UNL, CMA, Almada, Portugal

[2] FCT UNL, Dept Matemat, Almada, Portugal

关键词: Navier-Stokes equations;    Euler equations;    Stochastic differential equations;    Stochastic flows;    Lagrangian flows;    Large deviations principle;   

DOI  :  10.1016/j.jde.2017.12.031

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free