Wentzell-Freidlin Large Deviation Principle for the stochastic convective Brinkman-Forchheimer equations

TL;DR

This paper establishes a large deviation principle for solutions to the stochastic convective Brinkman-Forchheimer equations with Gaussian noise, providing insights into their asymptotic behavior and exit times.

Contribution

It introduces a Wentzell-Freidlin large deviation principle for the SCBF equations using a weak convergence approach, improving existing results for related fluid dynamics models.

Findings

Large deviation principle established for SCBF equations.

Exponential estimates on exit times derived.

Improves upon previous LDP results for Navier-Stokes related equations.

Abstract

This work addresses some asymptotic behavior of solutions to the stochastic convective Brinkman-Forchheimer (SCBF) equations perturbed by multiplicative Gaussian noise in bounded domains. Using a weak convergence approach of Budhiraja and Dupuis, we establish the Laplace principle for the strong solution to the SCBF equations in a suitable Polish space. Then, the Wentzell-Freidlin large deviation principle is derived using the well known results of Varadhan and Bryc. The large deviations for short time are also considered in this work. Furthermore, we study the exponential estimates on certain exit times associated with the solution trajectory of the SCBF equations. Using contraction principle, we study these exponential estimates of exit times from the frame of reference of Freidlin-Wentzell type large deviations principle. This work also improves several LDP results available in the literature for the tamed Navier-Stokes equations as well as Navier-Stokes equations with damping in bounded domains.