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We construct a solution to stochastic Navier-Stokes equations in dimension n≤4 with the feedback in both the external forces and a general infinite-dimensional noise. The solution is unique and adapted to the Brownian filtration in the 2-dimensional case with periodic boundary conditions or, when there is no feedback in the noise, for the Dirichlet boundary condition. The paper uses the methods of nonstandard analysis.
Acta Applicandae Mathematicae – Springer Journals
Published: May 3, 2004
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