A global existence result for the compressible Navier-Stokes-Poisson equations in three and higher dimensions (Q2893047)

The authors consider the Cauchy problem for the compressible barotropic Navier-Stokes-Poisson system in \(N\geq 3\) dimensions, in presence of an external field force \(f\in L^1({\mathbb R}^+;\dot{B}^{N/2-1}_{2,1})\), where \(\dot{B}^{N/2-1}_{2,1}\) is the homogeneous Besov space. They prove global existence and uniqueness of a strong solution in the framework of hybrid Besov spaces when data are close to a uniform rest state. This result extends a previous one by \textit{C. Hao} and \textit{H.-L. Li} [J. Differ. Equations 246, No. 12, 4791--4812 (2009; Zbl 1173.35098)] who considered the homogeneous case (\(f=0\)).