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.
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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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Ferrario, B., Zanella, M. Stochastic vorticity equation in \(\mathbb R^2\) with not regular noise. Nonlinear Differ. Equ. Appl. 25, 49 (2018). https://doi.org/10.1007/s00030-018-0541-7
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DOI: https://doi.org/10.1007/s00030-018-0541-7