Boundary Value Problems
Volume 2008 (2008), Article ID 735846, 14 pages
Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations
School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
Received 21 June 2007; Accepted 5 October 2007
Academic Editor: Colin Rogers
Copyright © 2008 Jianwen Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper is concerned with an initial boundary value problem in one-dimensional
magnetohydrodynamics. We prove the global existence, uniqueness, and stability of strong
solutions for the planar magnetohydrodynamic equations for isentropic compressible fluids in the
case that vacuum can be allowed initially.