Moderate deviation principle for the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity

TL;DR

This paper establishes a moderate deviation principle and a central limit theorem for 2D stochastic Navier-Stokes equations with anisotropic viscosity, advancing understanding of their probabilistic behavior.

Contribution

It introduces a moderate deviation principle for these equations using the weak convergence approach, which is a novel application in this context.

Findings

Proves a central limit theorem for the equations.

Establishes a moderate deviation principle using weak convergence.

Provides new insights into the probabilistic properties of anisotropic viscous flows.

Abstract

In this paper, we prove a central limit theorem and establish a moderate deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity. The proof for moderate deviation principle is based on the weak convergence approach.