Large deviation principle for occupation measures of two dimensional stochastic convective Brinkman-Forchheimer equations. Issue 2 (4th March 2023) - Kumar, Ankit; Mohan, Manil T.
Abstract: 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 in R 2 . We establish two important properties of the Markov semigroup associated with the solutions of 2 D 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 the ergodic behavior of 2 D 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.