1202.1382 (Quansen Jiu et al.)

Global well-posedness of 2D compressible Navier-Stokes equations with
large data and vacuum    [PDF]

Quansen Jiu, Yi Wang, Zhouping Xin

In this paper, we study the global well-posedness of the 2D 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 $\l$
is the power function of the density, that is, $\l(\r)=\r^\b$ with $\b>3$, then
the 2D compressible Navier-Stokes equations with the periodic boundary
conditions on the torus $\mathbb{T}^2$ admit a unique global classical solution
$(\r,u)$ which may contain vacuums in an open set of $\mathbb{T}^2$. Note that
the initial data can be arbitrarily large to contain vacuum states.

View original: http://arxiv.org/abs/1202.1382