Some results on the regularity of the equations of magneto-hydrodynamics

Regularity and spatial analyticity over the same time interval are established for the solutions of the MHD equations with zero viscosity and diffusivity. Global existence of a weak solution for positive viscosity and diffusivity is obtained. Global regularity and uniqueness are proved for large viscosity and diffusivity, and for all positive viscosity and diffusivity if in the two dissipative terms the Laplacian is raised to a power equal to or greater than (N plus 4)/2. For positive viscosity and zero diffusivity, global regularity and uniqueness are proved if in the viscous term the Laplacian is raised to a power greater than N/2 plus 1.