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This notes concern the sufficient conditions for regularity of solutions tothe evolution Navier-Stokes equations known in the literature as Prodi-Serrin'scondition. H.-O. Bae and H.-J. Choe proved in a 1999 paper that, in the wholespace R^3, it is merely sufficient that two components of the velocity satisfythe 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 velocitycomponent parallel to the boundary enjoys the above condition. Flat boundarygeometry seems not essential, as suggested by some preliminary calculations incylindrical domains.

On the extension to slip boundary conditions of a Bae and Choe regularity criterion for the Navier-Stokes equations. The half-space case