Existence of regular steady motions for a second-grade fluid with nonhomogeneous boundary conditions (Q1129790)

The title problem is investigated for Rivlin-Ericksen fluids in a not necessarily simply connected domain \(\Omega\subset\mathbb{R}^3\). It is not required that the velocity flux is vanishing on each component of \(\partial\Omega\). The authors apply a decomposition method, which permits to split the original nonlinear problem into two linear problems, namely a Stokes-like problem and a vector transport problem. The desired solution is then obtained as a fixed point of a specially constructed multivalued map.