Global large strong solution of the 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity

This paper concerns the Dirichlet problem of three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity. When the viscosity coefficient $\mu (\rho )$ is a power function of the density ($\mu (\rho )=\mu {\rho }^{\alpha }$ with $\alpha >1$), it is proved that the system will admit a unique global strong solution as long as the initial data are sufficiently large. This is the first result concerning the existence of large strong solution for the inhomogeneous Navier-Stokes equations in three dimensions.