Journal of Applied Mathematics and Stochastic Analysis 
Volume 13 (2000), Issue 3, Pages 239-259
doi:10.1155/S1048953300000228

Galerkin approximation and the strong solution of the Navier-Stokes equation

Hannelore Breckner

 Martin-Luther Universität Halle- Wittenberg, Fachbereich Mathematik und Informatik, Institut für Optimierung und Stochastik, Halle (Saale) D-06099, Germany
Received 1 June 1998; Revised 1 June 1999

Abstract

We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.