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

TL;DR

This paper proves a large deviation principle for 2D stochastic Navier-Stokes equations with anisotropic viscosity, addressing small noise and short time scenarios using weak convergence and exponential equivalence methods.

Contribution

It introduces the first large deviation principle for these equations with anisotropic viscosity, expanding stochastic fluid dynamics theory.

Findings

Large deviation principle established for small noise

Large deviation principle established for short time

Methodology based on weak convergence and exponential equivalence

Abstract

In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity both for small noise and for short time. The proof for large deviation principle is based on the weak convergence approach. For small time asymptotics we use the exponential equivalence to prove the result.