ON THE SELF-SIMILAR SOLUTIONS OF THE MAGNETO-HYDRO-DYNAMIC EQUATIONS |
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| Authors: | He Cheng Xin Zhouping |
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| Institution: | [1]Institute of Applied Mathematics, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing 100190, China [2]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 |
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| 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]. |
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| Keywords: | magneto-hydro-dynamics equations backward self-similar solutions forward self-similar solutions |
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