Large deviation principle for occupation measures of two dimensional stochastic convective Brinkman-Forchheimer equations

The present work is concerned about two-dimensional stochastic convective Brinkman-Forchheimer (2D SCBF) equations perturbed by a white noise (non degenerate) in smooth bounded domains in ${\mathbb{R}}^2$. We establish two important properties of the Markov semigroup associated with the solutions of 2D SCBF equations (for the absorption exponent $r=1,2,3$), that is, irreducibility and strong Feller property. These two properties implies the uniqueness of invariant measures and ergodicity also. Then, we discuss about the ergodic behavior of 2D SCBF equations by providing a Large Deviation Principle (LDP) for the occupation measure for large time (Donsker-Varadhan), which describes the exact rate of exponential convergence.