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We study the global existence and uniqueness of classical solutions to thethree-dimensional compressible isentropic Navier-Stokes equations with vacuumand external potential forces which could be arbitrarily large provided theinitial data is of small energy and the unique steady state is strictly awayfrom vacuum. In particular, the solution may have large oscillations andcontain vacuum states. For the case of discontinuous initial data, we alsoprove the global existence of weak solutions. The large-time behavior of thesolution is obtained simultaneously. It is worthwhile mentioning that thecompatibility condition on the initial data and the regularity condition of theexternal potential forces in the present paper are much weaker than thoseassumed in the existing literature.

On the motion of three-dimensional compressible isentropic flows with large external potential forces and vacuum