Abstract
Summary: We consider a family of boundary value problems for the
two-dimensional Stokes system on bounded domains $Ømega_R=Ømega\cap
G_R$. Here $Ømega$ is a domain with a compact complement and $G_R$
a bounded domain which blows up as $R\toınfty$ and contains the
boundary of $Ømega$ in its interior. The main results are uniform
estimates for the solutions on $Ømega_R$, where the dependence on
the parameter $R$ is calculated explicitly. The result is applied
to approximate solutions to the exterior Dirichlet problem for the
Stokes system by solutions on the bounded domains $Ømega_R$. Asymptotically
precise error estimates are derived.
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