Forward self-similar solutions to the MHD equations in the whole space

In this paper, we study the existence of forward self-similar solutions to the three-dimensional Magnetohydrodynamic equations (MHD equations) with arbitrarily large self-similar initial data. Using the so called blow-up argument, we establish the necessary a priori estimates. Subsequently, the Leray-Schauder theorem allows us to construct a self-similar solutions of the MHD equations.