Large deviations for the Boussinesq Equations under Random Influences

TL;DR

This paper establishes large deviation principles for a stochastic Boussinesq system modeling convection, using a weak convergence approach to analyze the probabilistic behavior of solutions under random influences.

Contribution

It introduces a novel application of weak convergence methods to derive large deviations for coupled stochastic PDEs in fluid dynamics.

Findings

Proved large deviation principles for stochastic Boussinesq equations.

Applied variational representation techniques to infinite-dimensional Brownian motion.

Enhanced understanding of probabilistic behavior in convection models under randomness.

Abstract

A Boussinesq model for the Benard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic Navier-Stokes equations and the transport equation for temperature. Large deviations are proved, using a weak convergence approach based on a variational representation of functionals of infinite dimensional Brownian motion.