Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On nonexistence of splash singularities for the $\alpha$-SQG patches   In this paper, we consider patch solutions to the $\alpha$-SQG equation and
derive new criteria for the absence of splash singularity where different
patches or parts of the same patch collide in finite time. Our criterion
refines a result due to Gancedo and Strain \cite{GS}, providing a condition on
the growth of curvature of the patch necessary for the splash and an
exponential in time lower bound on the distance between patches with bounded
curvature.

5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg