Global well-posedness for the two dimensional compressible MHD equations with large data

2012/04/25 by Dongfen Bian, Boling Guo, Bian, Dongfen +1
Engineering · Mathematics · #35Q35 #76N10 #76W05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1204.5608

openalex publication_date 2012/04/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we are concerned with the global well-posedness for the compressible MHD equations with large data. We show that if the shear viscosity μ is a positive constant and the bulk viscosity λ is the power function of the density, that is, λ(ρ)=ρ^β with β>3, then the two dimensional compressible MHD system with the periodic boundary conditions on the torus \mathbbT² have a unique global classical solution (ρ, u,H). In this work we extended the results about compressible Navier-Stokes equations in \citeKarzhikhov to compressible MHD equations by applying several new techniques to overcome the coupling between velocity and magnetic field.

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