A global existence result for the compressible Navier–Stokes–Poisson equations in three and higher dimensions
Volume 105 / 2012
Annales Polonici Mathematici 105 (2012), 179-198
MSC: Primary 35D35; Secondary 35Q30.
DOI: 10.4064/ap105-2-6
Abstract
The paper is dedicated to the global well-posedness of the barotropic compressible Navier–Stokes–Poisson system in the whole space $\mathbb{R}^{N}$ with $N\geq 3$. The global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces. The initial velocity has the same critical regularity index as for the incompressible homogeneous Navier–Stokes equations. The proof relies on a uniform estimate for a mixed hyperbolic/parabolic linear system with a convection term.
