Acta mathematica scientia, Series B >
ON THE SELF-SIMILAR SOLUTIONS OF THE MAGNETO-HYDRO-DYNAMIC EQUATIONS
Received date: 2008-10-27
Online 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
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].
HE Cheng , XIN Zhou-Beng . ON THE SELF-SIMILAR SOLUTIONS OF THE MAGNETO-HYDRO-DYNAMIC EQUATIONS[J]. Acta mathematica scientia, Series B, 2009 , 29(3) : 583 -598 . DOI: 10.1016/S0252-9602(09)60055-2
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