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Ergodicity for the 3D stochastic Navier–Stokes equations perturbed by Lévy noise
Author(s) -
Mohan Manil T.,
Sakthivel K.,
Sritharan Sivaguru S.
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700339
Subject(s) - mathematics , ergodic theory , semigroup , ergodicity , invariant measure , martingale (probability theory) , markov chain , mathematical analysis , navier–stokes equations , invariant (physics) , pure mathematics , mathematical physics , statistics , physics , compressibility , thermodynamics
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.