Existence theorem and blow-up criterion of the strong solutions to the two-fluid MHD equation in R3

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Abstract

We first give the local well-posedness of strong solutions to the Cauchy problem of the 3D two-fluid MHD equations, and then study the blow-up criterion of the strong solutions. By means of the Fourier frequency localization and Bony's paraproduct decomposition, it is proved that the strong solution (u,b) can be extended after t=T if either uLTq(B˙p,0) with 2q+3p1 and bLT1(B˙,0) or (ω,J)LTq(B˙p,0) with 2q+3p2, where ω(t)=×u denotes the vorticity of the velocity and J=×b stands for the current density.

MSC

76W05
35B65

Keywords

MHD equations
Well-posedness
Blow-up
Littlewood–Paley decomposition
Besov space

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