Regularity of axially symmetric flows in a half-space in three dimension

Abstract

We study axially symmetric solutions with no swirl of the three dimensional Navier-Stokes equations in a half-space. We prove that suitable weak solutions in this case are Hölder continuous up to the boundary at all points except for the origin. For interior points this implies smoothness in the spatial variables. Hölder continuity at the origin remains as an open problem.