Abstract
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.
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The research of this author was supported by an SERC Grant.
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Capiński, M., Cutland, N. Stochastic Navier-Stokes equations. Acta Appl Math 25, 59–85 (1991). https://doi.org/10.1007/BF00047665
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DOI: https://doi.org/10.1007/BF00047665