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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 ∥u0∥H32+ε+∥b0∥H2(0&lt;ε&lt;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.

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