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$$L^1$$ L 1 -Uniqueness of Kolmogorov Operators Associated with Two-Dimensional Stochastic Navier–Stokes Coriolis Equations with Space–Time White Noise

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  • Martin Sauer

    (Technische Universität Berlin)

Abstract

We consider the Kolmogorov operator $$K$$ K associated with a stochastic Navier–Stokes equation driven by space–time white noise on the two-dimensional torus with periodic boundary conditions and a rotating reference frame, introducing fictitious forces such as the Coriolis force. This equation then serves as a simple model for geophysical flows. We prove that the Gaussian measure induced by the enstrophy is infinitesimally invariant for $$K$$ K on finitely based cylindrical test functions, and moreover, $$K$$ K is $$L^1$$ L 1 -unique with respect to the enstrophy measure for sufficiently large viscosity.

Suggested Citation

  • Martin Sauer, 2016. "$$L^1$$ L 1 -Uniqueness of Kolmogorov Operators Associated with Two-Dimensional Stochastic Navier–Stokes Coriolis Equations with Space–Time White Noise," Journal of Theoretical Probability, Springer, vol. 29(2), pages 569-589, June.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0582-8
    DOI: 10.1007/s10959-014-0582-8
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    References listed on IDEAS

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    1. Albeverio, S. & Barbu, V. & Ferrario, B., 2008. "Uniqueness of the generators of the 2D Euler and Navier-Stokes flows," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2071-2084, November.
    2. Albeverio, Sergio & Høegh-Krohn, Raphael, 1989. "Stochastic flows with stationary distribution for two-dimensional inviscid fluids," Stochastic Processes and their Applications, Elsevier, vol. 31(1), pages 1-31, March.
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    1. Albeverio, S. & Barbu, V. & Ferrario, B., 2008. "Uniqueness of the generators of the 2D Euler and Navier-Stokes flows," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2071-2084, November.

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