Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability threshold for 2D shear flows of the Boussinesq system near
  Couette   In this paper, we consider the stability threshold for the shear flows of the
Boussinesq system in a domain $\mathbb{T} \times \mathbb{R}$. The main goal is
to prove the nonlinear stability of the shear flow $(U^S,\Theta^S)=((e^{\nu
t\partial_{yy}}U(y),0)^{\top},\alpha y)$ with $U(y)$ close to $y$ and
$\alpha\geq0$. We separate two cases: one is $\alpha\geq 0$ small scaling with
the viscosity coefficients and the case without smallness of $\alpha$ and fixed
heat diffusion coefficient. The novelty here is that we don't require $\mu=\nu$
and only need to assume that $\mu$ is scaled with $\nu$ or fixed, where $\mu$
is the inverse of the Reynolds number and $\nu $ is the heat diffusion
coefficient.

28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
3
The categories of this paper are: physics
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci