Gevrey well-posedness of the hydrostatic MHD-wave system

TL;DR

This paper proves local well-posedness in Gevrey space for a hydrostatic MHD-wave system with a degenerate hyperbolic magnetic field equation, addressing complex mathematical challenges.

Contribution

It establishes the first well-posedness result for this system in Gevrey class, handling the degeneracy of the magnetic field equation.

Findings

Local well-posedness in Gevrey 7/6 space for convex initial data

Use of boundary decomposition method to overcome degeneracy issues

Addresses mathematical difficulties due to degenerate hyperbolic equation

Abstract

This paper investigates the well-posedness of the hydrostatic MHD-wave system. Unlike the standard hydrostatic MHD equations, the tangential magnetic field equation in this system is degenerate hyperbolic rather than parabolic, which leads to substantial mathematical difficulties. Using the boundary decomposition method, we establish local well-posedness in Gevrey $\frac{7}{6}$ space for convex initial data.