Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness of the Cauchy problem of two-dimensional
  compressible Navier-Stokes equations in weighted spaces   In this paper, we study the global well-posedness of classical solution to 2D
Cauchy problem of the compressible Navier-Stokes equations with large initial
data and vacuum. It is proved that if the shear viscosity $\mu$ is a positive
constant and the bulk viscosity $\lambda$ is the power function of the density,
that is, $\lambda(\rho)=\rho^{\beta}$ with $\beta>3$, then the 2D Cauchy
problem of the compressible Navier-Stokes equations on the whole space
$\mathbf{R}^2$ admit a unique global classical solution $(\rho,u)$ which may
contain vacuums in an open set of $\mathbf{R}^2$. Note that the initial data
can be arbitrarily large to contain vacuum states. Various weighted estimates
of the density and velocity are obtained in this paper and these self-contained
estimates reflect the fact that the weighted density and weighted velocity
propagate along with the flow.

29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th