Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The It\^o SDEs and Fokker--Planck equations with Osgood and Sobolev
  coefficients   We study the degenerated It\^o SDE on $\mathbb R^d$ whose drift coefficient
only fulfills a mixed Osgood and Sobolev regularity. Under suitable assumptions
on the gradient of the diffusion coefficient and on the divergence of the drift
coefficient, we prove the existence and uniqueness of generalized stochastic
flows associated to such equations. We also prove the uniqueness of solutions
to the corresponding Fokker--Planck equation by using the probabilistic method.

29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc