Gevrey well-posedness of the hydrostatic MHD-wave system

2025/12/06 by Li, Wei-Xi, Xu, Zhan
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.2512.06405

openalex publication_date 2025/12/06 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28

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 (7)/(6) space for convex initial data.

Citations

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• Local well-posedness for the Hall-MHD system in optimal Sobolev Spaces
• Global well-posedness of an initial-boundary value problem for viscous non-resistive MHD systems