Stochastic 2D hydrodynamical type systems: Well posedness and large deviations

TL;DR

This paper establishes well-posedness and large deviation principles for a broad class of 2D hydrodynamical stochastic models, including Navier-Stokes, MHD, and Bénard problems, using weak convergence methods.

Contribution

It introduces a unified framework for analyzing well-posedness and large deviations in nonlinear stochastic 2D hydrodynamical models, extending previous results to a wider class.

Findings

Proved existence and uniqueness of solutions for the class of models.

Established a Wentzell-Freidlin type large deviation principle.

Applied weak convergence methods to stochastic hydrodynamical systems.

Abstract

We deal with a class of abstract nonlinear stochastic models, which covers many 2D hydrodynamical models including 2D Navier-Stokes equations, 2D MHD models and 2D magnetic B\'enard problem and also some shell models of turbulence. We first prove the existence and uniqueness theorem for the class considered. Our main result is a Wentzell-Freidlin type large deviation principle for small multiplicative noise which we prove by weak convergence method.