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Stochastic vorticity equation in \(\mathbb R^2\) with not regular noise

  • Benedetta Ferrario
  • Margherita Zanella
Article
  • 36 Downloads

Abstract

We consider the Navier–Stokes equations in vorticity form in \(\mathbb {R}^2\) with a white noise forcing term of multiplicative type, whose spatial covariance is not regular enough to apply the Itô calculus in \(L^q\) spaces, \(1<q<\infty \). We prove the existence of a unique strong (in the probability sense) solution.

Keywords

Stochastic vorticity equation \(\gamma \)-Radonifying operators Strong solution 

Mathematics Subject Classification

60H15 76D05 76M35 

Notes

Acknowledgements

This research was partially supported by INDAM-GNAMPA, PRIN 2015 “Determistic and stochastic evolution equations” and the Italian Ministry of Education, University and Research (MIUR) “Dipartimenti di Eccellenza Program” (2018–2022)—Dept. of Mathematics “F.Casorati”, University of Pavia.

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Authors and Affiliations

  1. 1.Dipartimento di Matematica “F. Casorati”Università di PaviaPaviaItaly
  2. 2.Dipartimento di Economia e FinanzaLibera Università degli Studi Sociali “G. Carli”RomeItaly

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