Full steady Stokes system in domains with cylindrical outlets (Q1298160)

The authors consider the full Stokes system \[ -\Delta v+\nabla p=f', \quad -\nabla \cdot v=f_4 \text{ in }\Omega,\quad v=g\text{ on }\partial \Omega\tag{1} \] in an unbounded doinain \(\Omega\subset\mathbb{R}^3\) which has cylindrical outlets at inifinity. They prove a representation formula and a priori estimates for solutions of (1) when the data \((f,g)\) belong to \(H^{l,q}\)-spaces. These results are generalized to function spaces with polynomial weights. The general procedure is to study the system first in a straight cylinder \(\omega\times\mathbb{R}\) by applying the Fourier transform in the third variable and then to extend the results to the more complicated geometry.