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

Abstract: This paper deals with the existence of global weak solutions for 3D MHD equations 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, we prove the existence of discretely self-similar solutions for 3D MHD equations for 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.