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

Abstract

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 $ł$ is the power function of the density, that is, $ł(\r)=\r^\b$ 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 $(\mathring{,}u)$ 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.

42 pages

References in corpus (1)

• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations

Cited by in corpus (1)

• A Note on Large Time Behavior of Velocity in the Baratropic Compressible Navier-Stokes Equations