Boundary partial regularity for the Navier–Stokes equations

We prove two conditions of local Hölder continuity for suitable weak solutions to the Navier–Stokes equations near the smooth curved part of the boundary of a domain. One of these condition has the form of the Caffarelli–Kohn–Nirenberg condition for the local boundedness of suitable weak solutions at the interior points of the space-time cylinder. The corresponding results near the plane part of the boundary were established earlier by G. Seregin.