Forward self-similar solutions of the MHD-boussinesq system with newtonian gravitational field

TL;DR

This paper proves the existence of forward self-similar solutions to the 3D MHD-Boussinesq system with gravity, using a blow-up argument and Leray-Schauder theorem, without small initial data assumptions.

Contribution

It establishes the existence of self-similar solutions for the MHD-Boussinesq system with gravity without requiring small initial conditions.

Findings

Existence of forward self-similar solutions proven.

Solutions constructed without smallness constraints.

Method employs blow-up argument and Leray-Schauder theorem.

Abstract

This paper is concerned with the existence of forward self-similar solutions to the three-dimensional Magnetohydrodynamic-Boussinesq (MHD-Boussinesq) system with 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.