Istituto di Matematica Applicata e Tecnologie Informatiche     
Ferrario B. Regularity results for stochastic Navier-Stokes equations. Preprint ercim.cnr.ian//1997-1054, 1997.
Regularity results for the 2D Navier-Stokes equations perturbed by a white noise term are presented. First of all, we remark that a cylindrical Wiener process is not enough to obtain any solution for the 2D case. Therefore, starting from the analysis of the problem under the weakest assumption on the noise, the framework to prove the existence of a weak solution is introduced. The study of the stochastic Navier-Stokes equations is divided into two subproblems; results on the linear Ornstein-Uhlenbeck equation are obtained by means of It^{o} calculus, whereas Galerkin method is applied to the other non-linear random equation. Moreover, regular solutions are investigated, obtaining strong and smooth solutions. According to the regularity of the covariance of the Wiener process, remarks on different results on the existence and/or uniqueness are provided.
Subject 65-XX

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