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.