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A note on stochastic Navier-Stokes equations with not regular multiplicative noise
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| Journal | Stochastic Partial Differential Equations: Analysis and Computations |
|---|---|
| Date | Accepted/In press - 14 Sep 2016 |
| Date | Published (current) - 20 Sep 2016 |
| Issue number | 1 |
| Volume | 5 |
| Number of pages | 28 |
| Pages (from-to) | 53-80 |
| Original language | English |
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 $d=2$.
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 $d=2$.
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
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