  This notes concern the sufficient conditions for regularity of solutions to
the evolution Navier-Stokes equations known in the literature as Prodi-Serrin's
condition. H.-O. Bae and H.-J. Choe proved in a 1999 paper that, in the whole
space R^3, it is merely sufficient that two components of the velocity satisfy
the above condition. Below, we extend the result to the half-space case R^n_+
under slip boundary conditions. We show that it is sufficient that the velocity
component parallel to the boundary enjoys the above condition. Flat boundary
geometry seems not essential, as suggested by some preliminary calculations in
cylindrical domains.
