Regularity of large solutions for the compressible magnetohydrodynamic equations

Xin Liu, Qin Yuming, Peng, Peng Xiaozhen

Description

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 H 1 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.

Informations

• Publié par: biomed
• Publié le: 01 janvier 2011
• Nombre de lectures: 7
• Langue: English

Extrait

Liu et al . Boundary Value Problems 2011, 2011 :30 http://www.boundaryvalueproblems.com/content/2011/1/30 R E S E A R C H Open Access Regularity of large solutions for the compressible magnetohydrodynamic equations 1* ng Qin 2 and Xiaozhen Peng 3 Xin Liu , Yumi * Correspondence: xinliu120@126. Abstract com 1 College of Information Sciences In this paper, we cons ar v and Technology, Donghua compressiblemagneto id h e y r dr t o h d e y i n n a iti m a i l- c b s o fl u o n w d s. y The al e u x e ist p e ro nc bl e e a m nd of c o o n nt e i - n d u i o m u e s nsional University, Songjiang Shanghai, 201620, People ’ s Republic of China dependence of global solutions in H 1 have been established in Chen and Wang (Z Full list of author information is Ange h P s 54, 608-632, 2003). We will obtain th available at the end of the article solutio w ns Ma u t nder hy certainassumptionsontheinitialdatab e y re d g e u ri l v a i r n it g y s o o f m gl e ob n a e l wapriori estimates. Keywords: magnetohydrodynamics (MHD), global solutions, regularity, initial-bound- ary value problem 1 Introduction Magnetohydrodynamics (MHD) is concerned with the flow of electrically conducting fluids in the presence of magnetic fields, either externally applied or generated within the fluid by inductive action. The application of magnetohydrodynamics covers a very wide range of physical areas from liquid metals to cosmic plasmas, for example, the intensely heated and ionized fluids in an electromagnetic field in astrophysics, geophy- sics, high-speed aerodynamics, and plasma physics. There is a complex interaction between the magnetic and fluid dynamic p henomena, and both hydrodynamic and electrodynamic effects have to be considered. For convenience, we consider the follow- ing plane magnetohydrodynamic equations in the Lagrangian coordinate system: v t − u y = 0, (1 : 1) u t + ( p + 2 1 | b | 2 ) y =  λ u y  y , (1 : 2) v w t − b y =  μ v w y  y , (1 : 3) (  ν v b y  y (1 : 4) v b ) t − w y = , E t +  u ( p + 1 2 | b | 2 ) − w · b  y =  λ uu y + μ w · w y v + ν b · b y + κθ y  y . (1 : 5) © 2011 Liu et al; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.