Existence of solutions for the magnetohydrodynamics with power-law type nonlinear viscous fluid

We are concerned with the existence of solutions for the magnetohydrodynamics with power-law type nonlinear viscous fluid in \({{\mathbb {R}}}^3\). We construct weak solutions for \(q>8/5\), and furthermore, in case \(q\ge 5/2\), we prove the existence of strong solutions.