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In this paper, we are concerned with the existence of global weak solutions to the compressible Navier–Stokes–Poisson equations with the non-flat doping profile when the viscosity coefficients are density-dependent, the data are large and spherically symmetric, and we focus on the case where those coefficients vanish in vacuum. We construct a suitable approximate system and consider it in annular regions between two balls. The global solutions are obtained as limits of such approximate solutions. Our proofs are mainly based on the energy and entropy estimates.

Global existence of weak solution for the compressible Navier–Stokes–Poisson system with density-dependent viscosity