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 μ is a positive constant and the bulk viscosity λ is the power function of the density, that is, λ(ρ) = ρ β with β > 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 (ρ, 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.