Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H\"{o}lder continuous weak solution of 2d Boussinesq equation with
  diffusive temperature   We show the existence of H\"{o}lder continuous periodic weak solutions of the
2d Boussinesq equation with diffusive temperature which satisfy the prescribed
kinetic energy. More precisely, for any smooth $e(t):[0,1]\rightarrow R_+$ and
$\varepsilon\in (0, \frac{1}{10})$, there exist $v\in
C^{\frac{1}{10}-\varepsilon}([0,1]\times {\rm T}^2), \theta\in
C_t^{1,\frac{1}{20}-\frac{\varepsilon}{2}}C_x^{2,\frac{1}{10}-\varepsilon}([0,1]\times
{\rm T}^2)$ which solve boussinesq equation in the sense of distribution and
satisfy e(t)=\int_{{\rm T}^2}|v(t,x)|^2dx, \quad \forall t\in [0,1].

6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci