Abstract
In this paper, we prove a new result on the properties of decay character $$r^*$$ (see Lemma 2.6) and then show a small data global well-posedness result for three-dimensional generalized incompressible Hall-MHD system. In the end, through Fourier splitting method, the properties of decay character $$r^*$$ and mathematical induction, we study the decay rate of higher-order spatial and time derivatives of strong solutions to such system.
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