Existence theorem and blow-up criterion of strong solutions to the two-fluid MHD equation in R 3

@inproceedings{Chen2007ExistenceTA,
  title={Existence theorem and blow-up criterion of strong solutions to the two-fluid MHD equation in R 3},
  author={Qionglei Chen and Changxing Miao},
  year={2007}
}
We first give the local well-posedness of strong solutions to the Cauchy problem of 3D two-fluid MHD equations, then study the blow-up criterion of strong solutions. By means of the Fourier frequency localization and Bony’s paraproduct decomposition, it is proved that strong solution (u, b) can be extended after t = T if either u ∈ LqT (Ḃ 0 p,∞) with 2 q + 3 p ≤ 1 and b ∈ LT (Ḃ 0 ∞,∞), or (ω, J) ∈ L q T (Ḃ 0 p,∞) with 2 q + 3 p ≤ 2, where ω(t) = ∇× u denotes the vorticity of the velocity and J… CONTINUE READING

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