The Annals of Probability

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

S. Albeverio and B. Ferrario

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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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Ann. Probab., Volume 32, Number 2 (2004), 1632-1649.

First available in Project Euclid: 18 May 2004

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Zentralblatt MATH identifier

Primary: 76D05: Navier-Stokes equations [See also 35Q30] 76M35: Stochastic analysis
Secondary: 74H25: Uniqueness of solutions 60G17: Sample path properties 60H15: Stochastic partial differential equations [See also 35R60]

Navier–Stokes equation space-time white noise pathwise uniqueness Gaussian invariant measure


Albeverio, S.; Ferrario, B. Uniqueness of solutions of the stochastic Navier–Stokes equation with invariant measure given by the enstrophy. Ann. Probab. 32 (2004), no. 2, 1632--1649. doi:10.1214/009117904000000379.

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