Uniqueness of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force

We prove uniqueness of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We make use of the Lagrangean framework in comparing the instantaneous states of corresponding fluid particles in two different solutions. The present work provides qualitative results on how the weak solutions depend continuously on initial data and steady states.