Stokes equations with interface condition in an unbounded domain

Abstract

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.

Keywords:

• Stokes equations
• decay estimates
• truncation error estimates

AMS Subject Classifications::

• 76D03
• 76D07