Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instability for Axisymmetric Blow-up Solutions to Incompressible Euler
  Equations   It is still not known whether a solution to the incompressible Euler
equation, endowed with a smooth initial value, can blow-up in finite time. In
[{\em Comm. Math. Phys.}, 378:557--568, 2020] it has been shown that, if it
exists, such a solution becomes linearly unstable close to the blow-up time. In
this paper, we show that the same phenomenon holds even in the more rigid
axisymmetric case. To obtain this result, we first prove a blow-up criterion
involving only the toroidal component of the vorticity. The instability of
blow-up profiles is also investigated.

10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex