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

Martin Sauer ()
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Martin Sauer: Technische Universität Berlin

Journal of Theoretical Probability, 2016, vol. 29, issue 2, 569-589

Abstract: 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.

Keywords: Kolmogorov operators; $$L^1$$ L 1 -uniqueness; Two-Dimensional stochastic Navier–Stokes equations with rotation; Gaussian invariant measures; 76D05; 60H15; 76B03; 76M35 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-014-0582-8

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