Forward self-similar solutions to the MHD-Boussinesq system with Newtonian gravitational field

Abstract

This paper is concerned with the existence of forward self-similar solutions to the three-dimensional Magnetohydrodynamic-Boussinesq (MHD-Boussinesq) system with a Newtonian gravitational field. By employing a blow-up argument and the Leray-Schauder theorem, we construct a forward self-similar solution to this system without imposing any smallness assumptions on the self-similar initial value.