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.
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Mohan, M. T., Sakthivel, K., & Sritharan, S. S. (2019). Ergodicity for the 3D stochastic Navier-Stokes equations perturbed by Lévy noise. Mathematische Nachrichten, 292(5), 1056–1088. https://doi.org/10.1002/mana.201700339