Global solutions to 3D compressible MHD equations with partial magnetic diffusion

Communications in Contemporary Mathematics 2026 Open access

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Authors: Jiahong Wu, Xiaoping Zhai
DOI: 10.1142/s0219199726500525
Cited by: 0

Abstract

The global existence of strong solutions to the compressible viscous magnetohydrodynamic (MHD) equations in [Formula: see text] remains a significant open problem. When there is no magnetic diffusion, even small data global well-posedness is unknown. This study investigates the Cauchy problem in [Formula: see text] for the compressible viscous MHD equations with horizontal magnetic diffusion. Using various anisotropic Sobolev inequalities and sharp estimates, we establish the existence of global solutions under small initial data within the Sobolev space framework.

Fields of Study & Subjects

Navier-Stokes equation solutions Advanced Mathematical Physics Problems Computational Fluid Dynamics and Aerodynamics

Publication details

Journal / source
Communications in Contemporary Mathematics
Publisher
World Scientific Pub Co Pte Ltd
Publication date
15 May 2026
Language
EN