Temporal decay of a global solution to 3D magnetohydrodynamic system in critical spaces

This paper considers the large time properties of global solutions to the 3D incompressible magnetohydrodynamic system in critical spaces $${\dot{H}}^\frac{1}{2}({\mathbb {R}}^3)$$ and $$L^3({\mathbb {R}}^3)$$ . More precisely, we obtain the temporal decay rate $$(1+t)^{-\frac{1}{4}}$$ for a small global solution in the space $${\dot{H}}^\frac{1}{2}({\mathbb {R}}^3)$$ , and a small global solution in the space $$L^3({\mathbb {R}}^3)$$ is non-increasing and decays to zero at infinity.