Existence and uniqueness of small energy weak solution to multi-dimensional compressible Navier-Stokes equations with large external potential force

We study the 3-D compressible Navier-Stokes equations with an external potential force and a general non-decreasing pressure. We prove the global-in-time existence of weak solutions with small-energy initial data and with densities being non-negative and essentially bounded. A solution may have large oscillations and contain vacuum states. No smallness assumption is made on the external force nor the initial perturbation in L∞ for density. Initial velocity u₀ is taken to be bounded in Lq for some q > 6 and no further regularity assumption is imposed on u₀. Finally, we discuss the uniqueness of weak solutions. Copyright © 2016 AIP Publishing.