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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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.

Article information

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

Dates
First available in Project Euclid: 18 May 2004

Permanent link to this document
https://projecteuclid.org/euclid.aop/1084884865

Digital Object Identifier
doi:10.1214/009117904000000379

Mathematical Reviews number (MathSciNet)
MR2060312

Zentralblatt MATH identifier
1065.60073

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.aop/1084884865


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References

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