The Navier-Stokes equations on a bounded domain

SupposeU is an open bounded subset of 3-space such that the boundary ofU has Lebesgue measure zero. Then for any initial condition with finite kinetic energy we can find a global (i.e. for all time) weak solutionu to the time dependent Navier-Stokes equations of incompressible fluid flow inU such that the curl ofu is continuous outside a locally closed set whose 5/3 dimensional Hausdorff measure is finite.This research was supported in part by the National Science Foundation Grant MCS-7903361