Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A study of energy concentration and drain in incompressible fluids   In this paper we examine two opposite scenarios of energy behavior for
solutions of the Euler equation. We show that if $u$ is a regular solution on a
time interval $[0,T)$ and if $u \in L^rL^\infty$ for some $r\geq
\frac{2}{N}+1$, where $N$ is the dimension of the fluid, then the energy at the
time $T$ cannot concentrate on a set of Hausdorff dimension samller than $N -
\frac{2}{r-1}$. The same holds for solutions of the three-dimensional
Navier-Stokes equation in the range $5/3<r<7/4$. Oppositely, if the energy
vanishes on a subregion of a fluid domain, it must vanish faster than
$(T-t)^{1-\d}$, for any $\d>0$. The results are applied to find new exclusions
of locally self-similar blow-up in cases not covered previously in the
literature.

19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga