Global well-posedness of strong solutions with large oscillations and vacuum to the compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile

Abstract

This paper concerns an initial value problem of compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile in whole space R3. The global well-posedness of strong solutions with large oscillations and vacuum is established, provided the initial data are of small energy and the steady state is strictly away from vacuum. A weak-strong uniqueness result is also obtained.