Journal of Theoretical Probability

, Volume 29, Issue 2, pp 569–589 | Cite as

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

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Abstract

We consider the Kolmogorov operator \(K\) 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 \(K\) on finitely based cylindrical test functions, and moreover, \(K\) is \(L^1\)-unique with respect to the enstrophy measure for sufficiently large viscosity.

Keywords

Kolmogorov operators \(L^1\)-uniqueness Two-Dimensional stochastic Navier–Stokes equations with rotation Gaussian invariant measures 

Mathematics Subject Classification (2010)

76D05 60H15 76B03 76M35 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany

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