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In this paper, we address the space-time decay properties for strongsolutions to the incompressible viscous resistive Hall-MHD equations. Weobtained the same space-time decay rates as those of the heat equation. Basedon the temporal decay results in \cite{cs}, we find that one can obtainweighted estimates of the magnetic field $B$ by direct weighted energyestimate, and then by regarding the magnetic convection term as a forcing termin the velocity equations, we can obtain the weighted estimates for thevorticity, which yields the corresponding estimates for the velocity field. Thehigher order derivative estimates will be obtained by using a parabolicinterpolation inequality proved in \cite{k01}. It should be emphasized that thethe magnetic field has stronger decay properties than the velocity field in thesense that there is no restriction on the exponent of the weight. The samearguments also yield the sharp space-time decay rates for strong solutions tothe usual MHD equations.

Space-time decay estimates for the incompressible viscous resistive Hall-MHD equations