Global Well-Posedness of 2D Compressible Navier–Stokes Equations with Large Data and Vacuum

摘要

In this paper, we study the global well-posedness of the 2D compressibleNavier-Stokes equations with large initial data and vacuum. It is proved thatif the shear viscosity $mu$ is a positive constant and the bulk viscosity $l$is the power function of the density, that is, $l()=^$ with $>3$, thenthe 2D compressible Navier-Stokes equations with the periodic boundaryconditions on the torus $mathbb{T}^2$ admit a unique global classical solution$(,u)$ which may contain vacuums in an open set of $mathbb{T}^2$. Note thatthe initial data can be arbitrarily large to contain vacuum states.