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Ergodicity of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noise

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  • Romito, Marco
  • Xu, Lihu

Abstract

We prove that any Markov solution to the 3D stochastic Navier-Stokes equations driven by a mildly degenerate noise (i.e. all but finitely many Fourier modes are forced) is uniquely ergodic. This follows by proving strong Feller regularity and irreducibility.

Suggested Citation

  • Romito, Marco & Xu, Lihu, 2011. "Ergodicity of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 673-700, April.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:4:p:673-700
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    References listed on IDEAS

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    1. Goldys, Benjamin & Röckner, Michael & Zhang, Xicheng, 2009. "Martingale solutions and Markov selections for stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1725-1764, May.
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