Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence and spatial analyticity for a nonlocal flux with
  fractional diffusion   In this paper, we study a one dimensional nonlinear equation with diffusion
$-\nu(-\partial_{xx})^{\frac{\alpha}{2}}$ for $0\leq \alpha\leq 2$ and $\nu>0$.
We use a viscous-splitting algorithm to obtain global nonnegative weak
solutions in space $L^1(\mathbb{R})\cap H^{1/2}(\mathbb{R})$ when
$0\leq\alpha\leq 2$. For subcritical $1<\alpha\leq 2$ and critical case
$\alpha=1$, we obtain global existence and uniqueness of nonnegative spatial
analytic solutions. We use a fractional bootstrap method to improve the
regularity of mild solutions in Bessel potential spaces for subcritical case
$1<\alpha\leq 2$. Then, we show that the solutions are spatial analytic and can
be extended globally. For the critical case $\alpha=1$, if the initial data
$\rho_0$ satisfies $-\nu<\inf\rho_0<0$, we use the characteristics methods for
complex Burgers equation to obtain a unique spatial analytic solution to our
target equation in some bounded time interval. If $\rho_0\geq0$, the solution
exists globally and converges to steady state.

29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph