A global existence result for the compressible Navier–Stokes–Poisson equations in three and higher dimensions

Zhensheng Gao¹ ; Zhong Tan²

¹School of Mathematical Sciences Xiamen University 361005 Xiamen, China and School of Mathematical Sciences Huaqiao University 362021 Quanzhou, China
²School of Mathematical Sciences Xiamen University 361005 Xiamen, China

Annales Polonici Mathematici, Tome 105 (2012) no. 2, pp. 179-198

Résumé

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.

Détail

DOI : 10.4064/ap105-2-6

Keywords: paper dedicated global well posedness barotropic compressible navier stokes poisson system whole space mathbb geq global existence uniqueness strong solution shown framework hybrid besov spaces initial velocity has critical regularity index incompressible homogeneous navier stokes equations proof relies uniform estimate mixed hyperbolic parabolic linear system convection term