Global Strong Solutions to the Cauchy Problem of Three-dimensional Isentropic Magnetohydrodynamics Equations with Large Initial Data

TL;DR

This paper proves the global existence of strong solutions for the three-dimensional isentropic compressible MHD equations with large initial data, including large initial velocities and magnetic fields, under certain density conditions.

Contribution

It establishes the existence of global strong solutions for 3D isentropic MHD equations with large initial data, relaxing previous size restrictions.

Findings

Global strong solutions exist for large initial data.

No restrictions on initial velocity and magnetic field sizes.

Solutions persist for all time under specified conditions.

Abstract

We consider the Cauchy problem to the three-dimensional isentropic compressible Magnetohydrodynamics (MHD) system with density-dependent viscosities. When the initial density is linearly equivalent to a large constant state, we prove that strong solutions exist globally in time, and there is no restriction on the size of the initial velocity and initial magnetic field.