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arXiv · 1510.03561

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

Zdzislaw Brzezniak·Benedetta Ferrario
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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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Zdzislaw Brzezniak, Benedetta Ferrario. 2015-10-13. A note on stochastic Navier-Stokes equations with not regular multiplicative noise. https://arxiv.org/abs/1510.03561

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