A note on stochastic Navier-Stokes equations with not regular multiplicative noise

Zdzislaw Brzezniak; Benedetta Ferrario

doi:10.1007/s40072-016-0081-2

A note on stochastic Navier-Stokes equations with not regular multiplicative noise

Zdzislaw Brzezniak, Benedetta Ferrario

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the Navier-Stokes equations in $\mathbb R^d$ ($d=2,3$) with
a stochastic forcing term which is white noise in time and coloured in space;
the spatial covariance of the noise is not too regular, so It\^o calculus cannot
be applied in the space of finite energy vector fields.
We prove existence of weak solutions for $d=2,3$ and pathwise uniqueness for $d=2$.

Original language	English
Pages (from-to)	53-80
Number of pages	28
Journal	Stochastic Partial Differential Equations: Analysis and Computations
Volume	5
Issue number	1
DOIs	https://doi.org/10.1007/s40072-016-0081-2
Publication status	Published - 20 Sept 2016

Bibliographical note

© Springer Science+Business Media New York 2016. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

Access to Document

10.1007/s40072-016-0081-2

Brz+Ferr_resubmit_07092016
© Springer Science+Business Media New York 2016. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details
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Cite this

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