Partial regularity of solutions to the Navier-Stokes equations

At the first instant of time when a viscous incompressible fluid flow with finite kinetic energy in three space becomes singular, the singularities in space are concentrated on a closed set whose one dimensional Hausdorff measure is finite. §1. Introduction. Let v: R3x R-+R3 (where R+= {t E R: t>0} represents time) be a weak solution to the Navier-Stokes equations of incompressible viscous fluid flow in 3 dimensional euclidean space with finite initial kinetic energy and viscosity equal to 1. Our