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Ergodicity for the 3D stochastic Navier–Stokes equations perturbed by Lévy noise

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  • Manil T. Mohan
  • K. Sakthivel
  • Sivaguru S. Sritharan

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.

Suggested Citation

  • Manil T. Mohan & K. Sakthivel & Sivaguru S. Sritharan, 2019. "Ergodicity for the 3D stochastic Navier–Stokes equations perturbed by Lévy noise," Mathematische Nachrichten, Wiley Blackwell, vol. 292(5), pages 1056-1088, May.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:5:p:1056-1088
    DOI: 10.1002/mana.201700339
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    Cited by:

    1. Mohan, Manil T., 2020. "Well posedness, large deviations and ergodicity of the stochastic 2D Oldroyd model of order one," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4513-4562.

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