Approximation of the Stokes Dirichlet problem in domains with cylindrical outlets

Let Omega subset of R-3 be a domain with J cylindrical outlets to infinity and u = (upsilon, p) be a solution of the Dirichlet problem for the Stokes system with prescibed flux H-j through the jth outlet. Let {Omega(R)} be the set of bounded domains defined by cutting each cylindrical outlet at the distance R from its origin. The problem investigated is how u can be approximated by solutions u(R) of boundary problems which are defined on the bounded subdomain Omega(R). On the artificial boundary partial derivative Omega(R)/partial derivative Omega a boundary condition Bu-R = h has to be added. By a method similar to the Schwartz' alternating method, the asymptotic behavior (as R tends to infinity) for u ? u(R) is investigated for different types of boundary conditions on the cut cross sections. The existence of solutions u(R) that are regular up to the edges is shown while using a boundary operator usually related to free boundary problems. For exponentially decaying data asymptotically precise estimates are derived for the difference u ? u(R); these results hold true for inhomogeneous boundary conditions on the lateral surface partial derivative Omega and nonvanishing divergence. For div upsilon = 0 and homogeneous boundary conditions on partial derivative Omega the case of L-2-forces also is examined.