Large data existence of global-in-time strong solutions to the incompressible Navier-Stokes equations in high space dimensions

We study the existence of strong solutions to the initial value problem for the incompressible Navier-Stokes equations in ℝ^N, N≥ 3. Our investigation shows that local in-time classical solutions do not develop singularity as long as the initial velocity lies in (L^2(ℝ^N))^N∩ (L^∞(ℝ^N))^N.