Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness for the incompressible Hall-MHD system with initial
  magnetic field belonging to $H^{\frac{3}{2}}(\mathbb{R}^3)$   In this paper, we first prove the local well-posedness of strong solutions to
the incompressible Hall-MHD system with initial data $(u_0,B_0)\in
H^{\frac{1}{2}+\sigma}(\mathbb{R}^3)\times H^{\frac{3}{2}}(\mathbb{R}^3)$ and
$\sigma\in (0,2)$. In particular, if the viscosity coefficient is equal to the
resistivity coefficient, we can reduce $\sigma$ to $0$ with the aid of the new
formulation of the Hall-MHD system observed by \cite{MR4193644}. Moreover, we
establish the global well-posedness in
$H^{\frac{1}{2}+\sigma}(\mathbb{R}^3)\times H^{\frac{3}{2}}(\mathbb{R}^3)$ with
$\sigma\in (0,2)$ for small initial data and get the optimal time-decay rates
of solutions. Our results improves some previous works.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph