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The barotropic compressible Navier-Stokes system with non-slip (Dirichlet)boundary conditions in a three-dimensional bounded domain is considered. Theglobal existence and uniqueness of classical solutions is obtained provided theinitial energy is properly small and the initial density is strictly away fromvacuum near the boundary of the domain. In particular, the density is allowedto vanish in the interior of the domain and its oscillations can be arbitrarilylarge. Moreover, a certain layering phenomenon occurs for the density, that is,the spatial gradient of the density remains uniformly bounded in some Lebesguespace with respect to time near the boundary and will grow unboundedly in thelong run with an exponential rate provided vacuum (even a point) appearsinitially in the interior of the domain. Finally, in order to make cleardistinction among the interior, intermediate, and the boundary parts of thedomain, Lagrangian coordinates are also applied in our calculations.

Global Classical Solutions to 3D Compressible Navier-Stokes System with Vacuum in Bounded Domains under Non-Slip Boundary Conditions