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

TY - JOUR

T1 - A note on stochastic Navier-Stokes equations with not regular multiplicative noise

AU - Brzezniak, Zdzislaw

AU - Ferrario, Benedetta

N1 - © 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

PY - 2016/9/20

Y1 - 2016/9/20

N2 - 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 $d=2$.

AB - 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 $d=2$.

U2 - 10.1007/s40072-016-0081-2

DO - 10.1007/s40072-016-0081-2

M3 - Article

SN - 2194-0401

VL - 5

SP - 53

EP - 80

JO - Stochastic Partial Differential Equations: Analysis and Computations

JF - Stochastic Partial Differential Equations: Analysis and Computations

IS - 1

ER -