Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The singularities for a periodic transport equation   In this paper, we consider a 1D periodic transport equation with nonlocal
flux and fractional dissipation $$
u_{t}-(Hu)_{x}u_{x}+\kappa\Lambda^{\alpha}u=0,\quad (t,x)\in R^{+}\times S, $$
where $\kappa\geq0$, $0<\alpha\leq1$ and $S=[-\pi,\pi]$. We first establish the
local-in-time well-posedness for this transport equation in $H^{3}(S)$. In the
case of $\kappa=0$, we deduce that the solution, starting from the smooth and
odd initial data, will develop into singularity in finite time. If adding a
weak dissipation term $\kappa\Lambda^{\alpha}u$, we also prove that the finite
time blowup would occur.

1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph