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

  • Zdzisław Brzeźniak
  • Benedetta FerrarioEmail author


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 Itô 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 \(d=2\).


Martingale solutions \(\gamma \)-radonifying operators Pathwise uniqueness 

Mathematics Subject Classification

76M35 76D05 60H15 



Part of this research started while Z. Brzeźniak was visiting the Department of Mathematics of the University of Pavia and was partially supported by the GNAMPA-INDAM project “Regolarità e dissipazione in fluidodinamica” and the PRIN 2010–2011; he would like to thank the hospitality of the Department.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsThe University of YorkYorkUK
  2. 2.Dipartimento di Matematica “F. Casorati”Università di PaviaPaviaItaly

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