Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hodge-theoretic analysis on manifolds with boundary, heatable currents,
  and Onsager's conjecture in fluid dynamics   We use Hodge theory and functional analysis to develop a clean approach to
heat flows and Onsager's conjecture on Riemannian manifolds with boundary,
where the weak solution lies in the trace-critical Besov space
$B_{3,1}^{\frac{1}{3}}$. We also introduce heatable currents as the natural
analogue to tempered distributions and justify their importance in Hodge
theory.

12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org