Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global stability of large solutions to the 3D compressible Navier-Stokes
  equations   The present paper aims at the investigation of the global stability of large
solutions to the compressible Navier-Stokes equations in the whole space. Our
main results and innovations can be concluded as follows:
  Under the assumption that the density $\rho(t,x)$ verifies $\rho(0,x)\ge c>0$
and $\sup_{t\ge0}\|\rho(t)\|_{C^\alpha}\le M$ with $\alpha$ sufficiently small,
we establish a new mechanism for the convergence of the solution to its
associated equilibrium with an explicit decay rate which is as the same as that
for the heat equation. The main idea of the proof relies on the basic energy
identity, techniques from blow-up criterion and a new estimate for the low
frequency part of the solution.
  We prove the global-in-time stability for the equations, i.e, any perturbed
solution will remain close to the reference solution if initially they are
close to each other. Our result implies that the set of the smooth and bounded
solutions is an open set.
  Going beyond the close-to-equilibrium setting, we construct the global large
solutions to the equations with a class of initial data in $L^p$ type critical
spaces. Here the "large solution" means that the vertical component of the
velocity could be arbitrarily large initially.

13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex