A removable singularity in a suitable weak solution to the Navier–Stokes equations

We formulate a new criterion for regularity of a suitable weak solution v to the Navier–Stokes equations at the point (x0, t0). We show that it is sufficient to impose conditions on the Serrin-type integrability of v and the associated pressure p in a parabolic neighbourhood of (x0, t0), intersected with the exterior of a certain space–time paraboloid with the vertex at point (x0, t0). We make no special assumptions on v or p in the interior of the paraboloid