Large deviation principle for occupation measures of two dimensional stochastic convective Brinkman-Forchheimer equations. Issue 2 (4th March 2023)

• Record Type: Journal Article
• Authors: Kumar, Ankit; Mohan, Manil T.
• Is Part Of: Stochastic analysis and applications. Volume 41:Issue 2(2023)
• Page Start: 214
• Page End: 256
• Publication Date: 2023-03-04
• Subjects: Stochastic convective Brinkman-Forchheimer equations -- irreducibility -- strong feller -- invariant measure -- large deviation principle; (2020): Primary 60F10 -- Secondary 60J35 -- 76D03 -- 37L40; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2021.2005626
• Languages: English
• ISSNs: 0736-2994

Abstract

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.