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Stokes equations with interface condition in an unbounded domain

We study stationary Stokes equations in an unbounded domain of ℝ3, with periodicity conditions on one part of the boundary, Dirichlet conditions on the other and a transmission condition. We show the existence and uniqueness of a solution which decays exponentially fast at infinity. We introduce an approximation process by solutions in bounded subdomains and establish asymptotically precise estimates for the truncation error. This gives rise to a practical numerical approximation method.