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 ${\parallel u_0\parallel }_{H^{\frac{3}{2}+\epsilon }}+{\parallel b_0\parallel }_{H^2}$$(0<\epsilon <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.

中文翻译：

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具有霍尔效应的3D磁感应方程的整体适定性和时间衰减

本文的主要目的是研究具有霍尔效应的三维不可压缩磁感应方程解的整体存在性和唯一性 ${\parallel {ü}_0\parallel }_{H^{\frac{3}{2}+\epsilon }}+{\parallel b_0\parallel }_{H^2}$$（0<\epsilon <\mathrm{1个}）$足够小。此外，使用傅立叶分裂法和衰减特性${\mathrm{[R}}^{*}$，还显示了具有霍尔效应的磁感应方程的解的高阶导数的代数衰减率。