Global classical solutions to the 2D compressible Navier-Stokes equations with vacuum

Abstract

We investigate the global classical solutions to the Cauchy problem for the 2-D viscous compressible Navier-Stokes equations with vacuum and small initial density but possibly large initial energy, provided the shear viscosity is a positive constant and the bulk one is λ = ρβ for any β ∈ [0, 1]. This extends the earlier work on the well-posedness theory of the compressible Navier-Stokes equations with small initial energy [such as Huang et al., Commun. Pure Appl. Math. 65, 549–585 (2012); Li and Xin, e-print arXiv:1310.1673; and Fang and Guo, Z. Angew. Math. Phys. 67, 22 (2016), respectively].