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Báo cáo hóa học: " Regularity of large solutions for the compressible magnetohydrodynamic equations"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài :Regularity of large solutions for the compressible magnetohydrodynamic equations | Liu et al. Boundary Value Problems 2011 2011 30 http www.boundaryvalueproblems.eom content 2011 1 30 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access Regularity of large solutions for the compressible magnetohydrodynamic equations Xin Liu1 Yuming Qin2 and Xiaozhen Peng3 Correspondence xinliu120@126. com 1College of Information Sciences and Technology Donghua University Songjiang Shanghai 201620 People s Republic of China Full list of author information is available at the end of the article Springer 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 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 geophysics high-speed aerodynamics and plasma physics. There is a complex interaction between the magnetic and fluid dynamic phenomena and both hydrodynamic and electrodynamic effects have to be considered. For convenience we consider the following plane magnetohydrodynamic equations in the Lagrangian coordinate system Vt Uy 0 1.1 ut p 1 I b 2 y 1.2 2 v y w b 1.3 vb t Wy 1.4 Vy Et u p 11 b 2 w b kuu WWy vb by . 1.5 2y Vy 2011 Liu et al licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons .