2D Navier–Stokes equation with cylindrical fractional Brownian noise

  • Benedetta FerrarioEmail author
  • Christian Olivera


We consider the Navier–Stokes equation on the 2D torus, with a stochastic forcing term which is a cylindrical fractional Wiener noise of Hurst parameter H. Following Albeverio and Ferrario (Ann Probab 32(2):1632–1649, 2004) and Da Prato and Debussche (J Funct Anal 196(1):180–210, 2002) which dealt with the case \(H=\frac{1}{2}\), we prove a local existence and uniqueness result when \(\frac{7}{16}< H<\frac{1}{2}\) and a global existence and uniqueness result when \(\frac{1}{2}<H<1\).


Stochastic partial differential equation Navier–Stokes equations Cylindrical fractional Brownian motion 

Mathematics Subject Classification

60H15 35R60 60H30 76D05 


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© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica “F. Casorati”Università di PaviaPaviaItaly
  2. 2.Departamento de MatemáticaUniversidade Estadual de CampinasCampinasBrazil

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