Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unique weak solutions of the non-resistive magnetohydrodynamic equations
  with fractional dissipation   This paper examines the uniqueness of weak solutions to the d-dimensional
magnetohydrodynamic (MHD) equations with the fractional dissipation
$(-\Delta)^\alpha u$ and without the magnetic diffusion. Important progress has
been made on the standard Laplacian dissipation case $\alpha=1$. This paper
discovers that there are new phenomena with the case $\alpha<1$. The approach
for $\alpha=1$ can not be directly extended to $\alpha<1$. We establish that,
for $\alpha<1$, any initial data $(u_0, b_0)$ in the inhomogeneous Besov space
$B^\sigma_{2,\infty}(\mathbb R^d)$ with $\sigma> 1+\frac{d}{2}-\alpha$ leads to
a unique local solution. For the case $\alpha\ge 1$, $u_0$ in the homogeneous
Besov space $\mathring B^{1+\frac{d}{2}-2\alpha}_{2,1}(\mathbb R^d)$ and $b_0$
in $ \mathring B^{1+\frac{d}{2}-\alpha}_{2,1}(\mathbb R^d)$ guarantees the
existence and uniqueness. These regularity requirements appear to be optimal.

17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess