Uniqueness of solutions of the stochastic Navier-Stokes equation with invariant measure given by the enstrophy
S. Albeverio, B. Ferrario
Abstract
A stochastic Navier-Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure μν whose covariance is given in terms of the enstrophy. Pathwise uniqueness for μν-a.e. initial velocity is proven for solutions having μν as invariant measure.
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