Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local regularity for the modified SQG patch equation   We study the patch dynamics on the whole plane and on the half-plane for a
family of active scalars called modified SQG equations. These involve a
parameter $\alpha$ which appears in the power of the kernel in their
Biot-Savart laws and describes the degree of regularity of the equation. The
values $\alpha=0$ and $\alpha=\frac 12$ correspond to the 2D Euler and SQG
equations, respectively. We establish here local-in-time regularity for these
models, for all $\alpha\in(0,\frac 12)$ on the whole plane and for all small
$\alpha>0$ on the half-plane. We use the latter result in [16], where we show
existence of regular initial data on the half-plane which lead to a finite time
singularity.

11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int