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

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 u is an element of L-T(q) ((B)over dot(p,infinity)(0)) with 2/q + 3/p <= 1 and b is an element of L-T(1) ((B)over dot(infinity,infinity)(0)) or (omega, J) is an element of L-T(q) ((B) over dot(p,infinity)(0)) with 2/q + 3/p <= 2, where omega(t) = del x u denotes the vorticity of the velocity and J = del x b stands for the current density. (c) 2007 Elsevier Inc. All rights reserved.