数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (3): 583-598.doi: 10.1016/S0252-9602(09)60055-2

• 论文 • 上一篇    下一篇

ON THE SELF-SIMILAR SOLUTIONS OF THE MAGNETO-HYDRO-DYNAMIC EQUATIONS

何成,辛周平   

  1. Department of Mathematics and The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China|Center for Nonlinear Studies, Northwest University, Xi’an 710069, China
  • 收稿日期:2008-10-27 出版日期:2009-05-20 发布日期:2009-05-20
  • 基金资助:

    The research of He is supported in part by The 973 key Program (2006CB805902), and Knowledge Innovation Funds of CAS(KJCX3-SYW-S03) , People’s Republic of China. The research of Xin is supported in part by the Zheng Ge Ru Foundation and Hong Kong RGC Earmarked Research Grants and a research grant from the Center on Nonlinear Studies, Northwest University

ON THE SELF-SIMILAR SOLUTIONS OF THE MAGNETO-HYDRO-DYNAMIC EQUATIONS

 HE Cheng, XIN Zhou-Beng   

  1. Department of Mathematics and The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China|Center for Nonlinear Studies, Northwest University, Xi’an 710069, China
  • Received:2008-10-27 Online:2009-05-20 Published:2009-05-20
  • Supported by:

    The research of He is supported in part by The 973 key Program (2006CB805902), and Knowledge Innovation Funds of CAS(KJCX3-SYW-S03) , People’s Republic of China. The research of Xin is supported in part by the Zheng Ge Ru Foundation and Hong Kong RGC Earmarked Research Grants and a research grant from the Center on Nonlinear Studies, Northwest University

摘要:

In this paper, we show that, for the three dimensional incompressible magneto-hydro-dynamic equations, there exists only trivial backward self-similar solution in Lp(R3) for p  3, under some smallness assumption on either the kinetic energy of the self-similar solution related to the velocity field, or the magnetic field. Second, we construct a class of global unique forward self-similar solutions to the three-dimensional MHD equations with
small initial data in some sense, being homogeneous of degree −1 and belonging to some Besov space, or the Lorentz space or pseudo-measure space, as motivated by the work in[5].

关键词: magneto-hydro-dynamics equations, backward self-similar solutions, forward self-similar solutions

Abstract:

In this paper, we show that, for the three dimensional incompressible magneto-hydro-dynamic equations, there exists only trivial backward self-similar solution in Lp(R3) for p  3, under some smallness assumption on either the kinetic energy of the self-similar solution related to the velocity field, or the magnetic field. Second, we construct a class of global unique forward self-similar solutions to the three-dimensional MHD equations with
small initial data in some sense, being homogeneous of degree −1 and belonging to some Besov space, or the Lorentz space or pseudo-measure space, as motivated by the work in[5].

Key words: magneto-hydro-dynamics equations, backward self-similar solutions, forward self-similar solutions

中图分类号: 

  • 35Q