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Global classical solutions to compressible Navier-Stokes equations with vacuum

In this paper, we establish the existence of a global classical solution to 3D Cauchy problem of the isentropic compressible Navier-Stokes equations with large initial data and vacuum under the assumption that $(\gamma-1)^\frac{1}{6}E_0^{\frac{1}{2}}\mu^{-\frac{1}{2}}$ is suitably small. It is showed that the initial energy $E_0$ can be large if the adiabatic exponent $\gamma$ is near $1$ or the viscosity coefficient $\mu$ is taken to be large. This is a joint work with Xiaofeng Hou and Hongyun Peng.