Abstract
Abstract
This paper proves the uniqueness of measure for time-inhomogeneous random
dynamical systems that exhibit particular controllability and coupling
conditions. This is done by extending a result for uniqueness of measure for timehomogeneous
Markov processes to the time-inhomogeneous case, showing that
the Markov process is exponentially mixing in the dual-Lipschitz norm. It is then
shown that the 2D Navier-Stokes equations on the sphere with a time-dependent
deterministic force and a ”kick”-type random perturbation satisfy the conditions
and thus have a unique limiting measure.
MSC Classification: 35Q30 , 60H15 , 60J05 , 93C20 , 35R01 , 60J99
Publisher
Research Square Platform LLC
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