Ergodicity for the 3D stochastic Navier–Stokes equations perturbed by Lévy noise. Issue 5 (5th December 2018)

• Record Type: Journal Article
• Authors: Mohan, Manil T.; Sakthivel, K.; Sritharan, Sivaguru S.
• Is Part Of: Mathematische Nachrichten. Volume 292:Issue 5(2019)
• Page Start: 1056
• Page End: 1088
• Publication Date: 2018-12-05
• Subjects: ergodicity -- invariant measures -- Lévy noise -- Markov solutions -- stochastic Navier–Stokes equations -- 35Q10 -- 37L40 -- 60H15 -- 60J75; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201700339
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract: In this work we construct a Markov family of martingale solutions for 3D stochastic Navier–Stokes equations (SNSE) perturbed by Lévy noise with periodic boundary conditions. Using the Kolmogorov equations of integrodifferential type associated with the SNSE perturbed by Lévy noise, we construct a transition semigroup and establish the existence of a unique invariant measure. We also show that it is ergodic and strongly mixing.