  The choice of the boundary conditions in mechanical problems has to reflect
the interaction of the considered material with the surface, despite the
assumption of the no-slip condition is preferred to avoid boundary terms in the
analysis and slipping effects are usually overlooked. Besides the "static slip
models", there are phenomena not accurately described by them, e.g. in the
moment when the slip changes rapidly, the wall shear stress and the slip can
exhibit a sudden overshoot and subsequent relaxation. When these effects become
significant, the so-called dynamic slip phenomenon occurs. We develop a
mathematical analysis of Navier-Stokes-like problems with dynamic slip boundary
condition, which requires a proper generalisation of the Gelfand triplet and
the corresponding function spaces setting.
