Formation of Finite Time Singularity for Axially Symmetric Magnetohydrodynamic Waves in 3-D

TL;DR

This paper proves that finite-time singularities can form in three-dimensional axisymmetric compressible magnetohydrodynamics equations, highlighting the role of magnetic forces under symmetry assumptions.

Contribution

It demonstrates finite-time singularity formation in 3D axisymmetric MHD equations, utilizing the structure of magnetic forces and axisymmetry assumptions.

Findings

Finite-time singularity formation is proved for axisymmetric initial data.

Magnetic force structure plays a crucial role in singularity development.

Results contribute to understanding plasma behavior in magnetohydrodynamics.

Abstract

In this paper we study the compressible magnetohydrodynamics equations in three dimensions, which offer a good model for plasmas. Formation of singularity for C1-solution in finite time is proved with axisymmetric initial data. The key observation is that the magnetic force term admits good structure with axisymmtric assumption.