Jamel Benameur and Ridha Selmi

Anisotropic Rotating MHD System in Critical Anisotropic Spaces

abstract:
The three-dimensional mixed (parabolic-hyperbolic) nonlinear magnetohydrodynamic system is investigated in the whole space $\mathbb{R}^3$. Uniqueness is proved in the anisotropic
Sobolev space $H^{0,\frac{1}{2}}$. Existence and uniqueness are proved in the anisotropic mixed Besov-Sobolev space ${\mathcal B^{0,\frac{1}{2}}}$. 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.

Mathematics Subject Classification: 35A05, 35A07, 35B40

Key words and phrases: Mixed (parabolic-hyperbolic) MHD system, existence, uniqueness, critical spaces, Strichartz inequality, asymptotic behavior