Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence theorem and blow-up criterion of strong solutions to the
  two-fluid MHD equation in ${\mathbb R}^3$   We first give the local well-posedness of strong solutions to the Cauchy
problem of the 3D two-fluid MHD equations, 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 strong solution $(u,b)$ can be
extended after $t=T$ if either $u\in L^q_T(\dot B^{0}_{p,\infty})$ with
$\frac{2}{q}+\frac{3}{p}\le 1$ and $b\in L^1_T(\dot B^{0}_{\infty,\infty})$, or
$(\omega, J)\in L^q_T(\dot B^{0}_{p,\infty})$ with $\frac{2}{q}+\frac{3}{p}\le
2$, where $\omega(t)=\na\times u $ denotes the vorticity of the velocity and
$J=\na\times b$ the current density.

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The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci