On the construction of the Stokes flow in a domain with cylindrical ends

Based on existence results for the Stokes operator and its solution properties in manifolds with cylindrical ends by Große et al. and Kohr et al., the Stokes flow in a three‐dimensional compact domain Ω+$$ {\Omega}^{+} $$ with circular openings Σj(j=1,2)$$ {\Sigma}_j\kern0.1em \left(j=1,2\right) $$ through which the fluid enters and leaves Ω+$$ {\Omega}^{+} $$ through unbounded cylindrical pipes the Stokes flow is modeled as a mixed boundary value problem Ω+$$ {\Omega}^{+} $$ whereas in the cylindrical ends, the velocities and pressures are constant on every straight line in the cylindrical directions with initial values from the openings Σj$$ {\Sigma}_j $$ of Ω+$$ {\Omega}^{+} $$. These values equal the velocities and pressures which are obtained from the mixed boundary values' solution in Ω+$$ {\Omega}^{+} $$ at the openings Σj$$ {\Sigma}_j $$.