Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Markov semi-groups generated by elliptic operators with divergence-free
  drift   In this paper we construct a conservative Markov semi-group with generator
$L=\Delta+b\cdot\nabla$ on $\mathbb{R}^n$, where $b$ is a divergence-free
vector field which belongs to $L^{2}\cap L^{p}$ with $\frac{n}{2}<p$. The
research is motivated by the question of understanding the blow-up solutions of
the fluid dynamic equations, which attracts a lot of attention in recent years.

28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
16
The categories of this paper are: stat
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org