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

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

2004-10-06

arxiv.org/abs/math/0410158v1

Annals of Probability 2004, Vol. 32, No. 2, 1632-1649

Mathematics

Probability

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imsta

Scientific paper

10.1214/009117904000000379

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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