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.

arXiv comment42 pages

References in corpus (3)

• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations
• A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations
• On the motion of three-dimensional compressible isentropic flows with large external potential forces and vacuum

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