Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations | Hindawi Publishing Corporation Boundary Value Problems Volume 2008 Article ID 735846 14 pages doi 2008 735846 Research Article Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations Jianwen Zhang School of Mathematical Sciences Xiamen University Xiamen 361005 China Correspondence should be addressed to Jianwen Zhang jwzhang@ Received 21 June 2007 Accepted 5 October 2007 Recommended by Colin Rogers 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. 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. 1. Introduction Magnetohydrodynamics MHD concerns the motion of a conducting fluid in an electromagnetic field with a very wide range of applications. The dynamic motion of the fluids and the magnetic field strongly interact each other and thus both the hydrodynamic and electrodynamic effects have to be considered. The governing equations of the plane magnetohydrodynamic compressible flows have the following form see . 1-5 Pt pu x 0 pA pu2 p 2 b ộ iux x pwf puw - b x ffwx x bt ub - w x ybx x pe t peù x - Kex x Xu2 pịwxỊ2 u bx12 - pux where p denotes the density of the fluid u G R the longitudinal velocity w w1 w2 G R2 the transverse velocity b b1 b2 G R2 the transverse magnetic field Ỡ the temperature 2 Boundary Value Problems p p p ỡ the pressure and e e p ỡ the internal energy X and p are the bulk and shear viscosity coefficients V is the magnetic viscosity K is the heat conductivity. Notice that the longitudinal magnetic field is a constant which is taken to be .
