Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Onsager's Conjecture for the Incompressible Euler Equations in Bounded
  Domains   The goal of this note is to show that, also in a bounded domain $\Omega
\subset \mathbb{R}^n$, with $\partial \Omega\in C^2$, any weak solution,
$(u(x,t),p(x,t))$, of the Euler equations of ideal incompressible fluid in
$\Omega\times (0,T) \subset \mathbb{R}^n\times\mathbb{R}_t$, with the
impermeability boundary condition: $u\cdot \vec n =0$ on
$\partial\Omega\times(0,T)$, is of constant energy on the interval $(0,T)$
provided the velocity field $u \in L^3((0,T);
C^{0,\alpha}(\overline{\Omega}))$, with $\alpha>\frac13\,.$

22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th