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

Zdzislaw Brzezniak, Benedetta Ferrario

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)53-80
Number of pages28
JournalStochastic Partial Differential Equations: Analysis and Computations
Issue number1
Publication statusPublished - 20 Sept 2016

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