Abstract
The three-dimensional mixed (parabolic-hyperbolic) nonlinear magnetohydrodynamic system is investigated in the whole space R-3 Uniqueness is proved in the anisotropic Sobolev space H-0,H-1/2. Existence and uniqueness are proved in the anisotropic mixed Besov-Sobolev space B-0,B-1/2. Asymptotic behavior is investigated as the Rossby number goes to zero. Energy methods, Freidrichs scheme, compactness arguments, anisotropic Littlewood-Paley theory, dispersive methods and Strichartz inequality are used.