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

The present work is concerned with two-dimensional stochastic subcritical and critical convective Brinkman-Forchheimer (2 D SCBF) equations perturbed by a white noise (non-degenerate) in smooth bounded domains R2. We establish two important properties of the Markov semigroup associated solutions 2 SCBF (for absorption exponent r = 1, 2, 3), that is, irreducibility strong Feller property. These implies uniqueness invariant measures ergodicity also. Then, we discuss ergodic behavior providing Large Deviation Principle (LDP) for occupation measure large time (Donsker-Varadhan), which describes exact rate exponential convergence.