【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
【机 构】
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Institute of Applied Mathematics,Department of Mathematics and The Institute of Mathematical Science
【基金项目】
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国家重点基础研究发展规划(973计划);Knowledge Innovation Funds of CAS;Zheng Ge Ru Foundation;Hong Kong RGC Earmarked Research Grants;Center on Nonlinear Studies, Northwest University
论文部分内容阅读
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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