Large deviations principle for the invariant measures of the 2D\n stochastic Navier-Stokes equations with vanishing noise correlation

2020/12/29 by Sandra Cerrai, Cerrai, Sandra, Nicholas Paskal +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · Engineering · #Stochastic processes and financial applications #Navier-Stokes equation solutions #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.2012.14953

Abstract

We study the two-dimensional incompressible Navier-Stokes equation on the\ntorus, driven by Gaussian noise that is white in time and colored in space. We\nconsider the case where the magnitude of the random forcing \√( e) and its\ncorrelation scale \δ( e) are both small. We prove a large deviations\nprinciple for the solutions, as well as for the family of invariant measures,\nas e and \δ( e) are simultaneously sent to 0, under a suitable\nscaling.\n

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