Large deviations for 2D Stochastic Chemotaxis-Navier-Stokes System

TL;DR

This paper proves a large deviation principle for the 2D stochastic Chemotaxis-Navier-Stokes system with small noise, overcoming challenges related to compactness and equation complexity.

Contribution

It introduces novel methods involving finite dimensional projections and stopping times to establish large deviations for complex stochastic PDEs.

Findings

Large deviation principle established for the 2D stochastic Chemotaxis-Navier-Stokes system

Overcomes compactness issues using finite dimensional projections

Employs stopping times to handle equation complexity

Abstract

In this paper, we establish a large deviation principle for 2D stochastic Chemotaxis-Navier-Stokes equation perturbed by a small multiplicative noise. The main difficulties come from the lack of a suitable compact embedding into the space occupied by the solutions and the inherent complexity of equation. Finite dimensional projection arguments and introducing suitable stopping times play important roles.