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

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JournalStochastic Partial Differential Equations: Analysis and Computations
DateAccepted/In press - 14 Sep 2016
DatePublished (current) - 20 Sep 2016
Issue number1
Volume5
Number of pages28
Pages (from-to)53-80
Original languageEnglish

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 $d=2$.

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