The Navier-Stokes equations on a bounded domain

Suppose U is an open bounded subset of 3-space such that the boundary of U has Lebesgue measure zero. Then for any initial condition with finite kinetic energy we can find a global (i.e. for all time) weak solution u to the time dependent Navier-Stokes equations of incompressible fluid flow in U such that the curl of u is continuous outside a locally closed set whose 5/3 dimensional Hausdorff measure is finite. (orig.)