Asymptotics of stochastic 2D Hydrodynamical type systems in unbounded domains

TL;DR

This paper establishes a central limit theorem and a moderate deviation principle for 2D stochastic hydrodynamical systems with multiplicative noise in unbounded domains, covering models like Navier-Stokes, MHD, and turbulence shell models.

Contribution

It introduces new asymptotic results for a broad class of 2D stochastic hydrodynamical systems, including several important physical models.

Findings

Proves a central limit theorem for these systems.

Establishes a moderate deviation principle using weak convergence.

Applies to models like Navier-Stokes, MHD, and Bénard problems.

Abstract

In this paper, we prove a central limit theorem and establish a moderate deviation principle for 2D stochastic hydrodynamical type systems with multiplicative noise in unbounded domains, which covers 2D Navier-Stokes equations, 2D MHD models and the 2D magnetic B?enard problem and also shell models of turbulence. The weak convergence method plays an important role in obtaining the moderate deviation principle.