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

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

2012-02-07

arxiv.org/abs/1202.1382v1

Mathematics

Analysis of PDEs

42 pages

Scientific paper

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.

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