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This paper deals with the existence of global weak solutions for 3D MHDequations when the initial data belong to the weighted spaces $L^2_{w_\gamma}$,with $w_\gamma(x)=(1+| x|)^{-\gamma}$ and $0 \leq \gamma \leq 2$. Moreover, weprove the existence of discretely self-similar solutions for 3D MHD equationsfor discretely self-similar initial data which are locally square integrable.Our methods are inspired of a recent work of P. Fern\'andez-Dalgo and P.G.Lemari\'e-Riseusset for the 3D Navier-Stokes equations.

Existence of infinite-energy and discretely self-similar global weak solutions for 3D MHD equations