Well-posedness for Hall-magnetohydrodynamics

2012/12/17 by Dongho Chae, Pierre Degond, Chae, Dongho +3 · 5 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · doi:10.48550/arxiv.1212.3919

openalex publication_date 2012/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove local existence of smooth solutions for large data and global smooth solutions for small data to the incompressible, resitive, viscous or inviscid Hall-MHD model. We also show a Liouville theorem for the stationary solutions.

Cited by

• The incompressible limit of the Euler-Maxwell two-fluid system
• Well-posedness of the relaxed Electron MHD equations with random diffusion
• Non-uniqueness of weak solutions to the 3D Hall-MHD equations on the plane
• On the temporal decay for the Hall-magnetohydrodynamic equations
• On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics

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• Global smooth solutions of the 3D Hall-magnetohydrodynamic equations\n with large data