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Uniqueness of solutions of the stochastic Navier-Stokes equation with invariant measure given by the enstrophy

S. Albeverio·B. Ferrario
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Abstract

A stochastic Navier-Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure \mu_{\nu} whose covariance is given in terms of the enstrophy. Pathwise uniqueness for \mu_{\nu}-a.e. initial velocity is proven for solutions having \mu_{\nu} as invariant measure.

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S. Albeverio, B. Ferrario. 2004-10-06. Uniqueness of solutions of the stochastic Navier-Stokes equation with invariant measure given by the enstrophy. https://doi.org/10.1214/009117904000000379

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