On Global Well-Posedness and Temporal Decay for 3D Magnetic Induction Equations with Hall Effect.

The main purpose of this paper is to study the global existence and uniqueness of solutions for three-dimensional incompressible magnetic induction equations with Hall effect provided that ∥ u 0 ∥ H 3 2 + ε + ∥ b 0 ∥ H 2 (0 < ε < 1) is sufficiently small. Moreover, using the Fourier splitting method and the properties of decay character r * , one also shows the algebraic decay rate of a higher order derivative of solutions to magnetic induction equations with the Hall effect. [ABSTRACT FROM AUTHOR]