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Open Access Research

Regularity of large solutions for the compressible magnetohydrodynamic equations

Xin Liu1*, Yuming Qin2 and Xiaozhen Peng3

Author affiliations

1 College of Information Sciences and Technology, Donghua University, Songjiang Shanghai, 201620, People's Republic of China

2 Department of Applied Mathematics, College of Sciences, Donghua University, Songjiang Shanghai 201620, People's Republic of China

3 Songyin School, Jinshan Shanghai, 201504, People's Republic of China

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Citation and License

Boundary Value Problems 2011, 2011:30  doi:10.1186/1687-2770-2011-30

Published: 10 October 2011

Abstract

In this paper, we consider the initial-boundary value problem of one-dimensional compressible magnetohydrodynamics flows. The existence and continuous dependence of global solutions in H1 have been established in Chen and Wang (Z Angew Math Phys 54, 608-632, 2003). We will obtain the regularity of global solutions under certain assumptions on the initial data by deriving some new a priori estimates.

Keywords:
magnetohydrodynamics (MHD); global solutions; regularity; initial-boundary value problem