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

doi:10.1016/S0252-9602(09)60055-2

Abstract

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

CLC Number:

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.

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