Well-posedness of linearized Taylor equations in magnetohydrodynamics

TL;DR

This paper establishes the well-posedness of a linearized version of the Taylor model derived from magnetohydrodynamics equations, relevant to Earth's magnetic field, as an initial step in understanding the nonlinear system.

Contribution

It proves well-posedness for a simplified linearization of the Taylor model in magnetohydrodynamics, advancing theoretical understanding of the system.

Findings

Well-posedness of the linearized Taylor equations is demonstrated.

Provides a mathematical foundation for further nonlinear analysis.

Connects the model to Earth's magnetic field dynamics.

Abstract

This paper is a first step in the study of the so-called Taylor model, introduced by J.B. Taylor in \cite{Taylor}. This system of nonlinear PDE's is derived from the viscous incompressible MHD equations, through an asymptotics relevant to the Earth's magnetic field. We consider here a simple class of linearizations of the Taylor model, for which we show well-posedness.