Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness in Gevrey function space for the three-dimensional
  Prandtl equations   In the paper, we study the three-dimensional Prandtl equations without any
monotonicity condition on the velocity field. We prove that when one tangential
component of the velocity field has a single curve of non-degenerate critical
points with respect to the normal variable, the system is locally well-posed in
the Gevrey function space with Gevrey index in $]1, 2].$ The proof is based on
some new observation of cancellation mechanism in the three space dimensional
system in addition to those in the two-dimensional setting obtained in
[1,7,19,22].

28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess