Space-Time Regularity for the Three Dimensional Navier-Stokes and MHD Equations

In this paper, we investigate the space-time regularity of solutions to (1) the three dimensional incompressible Navier-Stokes equations for initial data u(0) = (u(0)(h), u(0)(3)) is an element of (B) over dot(p,r)(3/p-1) (R-3) with large initial vertical velocity component; and (2) the three dimensional incompressible magneto-hydrodynamic equations for initial datum u(0) = (u(0)(h), u(0)(3)) is an element of(B) over dot(p,r)(3/p-1)(R-3) with large initial vertical velocity component and b(0) = (b(0)(h), b(0)(3)) is an element of(B) over dot(p,r)(3/p-1)(R-3) with large initial vertical magnetic field component.