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

References in corpus (8)

• Large deviations for infinite dimensional stochastic dynamical systems
• Stochastic 2D hydrodynamical type systems: Well posedness and large deviations
• Local and global well-posedness of SPDE with generalized coercivity conditions
• Energy equality for the 3D critical convective Brinkman-Forchheimer equations
• $\gamma$-Radonifying operators -- a survey
• Stochastic tamed Navier-Stokes equations on ${\mathbb{R}}^3$:existence, uniqueness of solution and existence of an invariant measure
• Stochastic convective Brinkman-Forchheimer equations on general Unbounded Domains
• 3D tamed Navier-Stokes equations driven by multiplicative Lévy noise: Existence, uniqueness and large deviations

Cited by in corpus (2)

• Martingale solution, invariant measure and ergodicity for stochastic convective Brinkman-Forchheimer equations on general domains in ${\mathbb{R}}^d$
• Global well-posedness and small time asymptotics of stochastic Ladyzhenskaya-Smagorinsky equations with damping on unbounded domains