Local and global existence for the coupled Navier-Stokes-Poisson problem

Abstract

Abstract.In this paper we investigate the Cauchy Problem for coupled NavierStokes-Poisson equation. The global existence of weak solutions in Sobolev framework is proved by using some compactification properties deduced from the Poisson equation.

Asymptotic compactness of global trajectories generated by the Navier–Stokes–Poisson equations of a compressible fluid

“…The reader can refer to for instance [6,18], and references therein for details. In Donatelli [6], gave the existence of local and global weak solutions for the bounded domain case.…”

“…The reader can refer to for instance [6,18], and references therein for details. In Donatelli [6], gave the existence of local and global weak solutions for the bounded domain case. And the authors [18] studied the optimal decay rate of the density and momentum of the compressible Navier-Stokes-Poisson system in R 3 .…”

From the dynamics of gaseous stars to the incompressible Euler equations

“…The heat flux q is proportional to the spatial gradient of the temperature and is given by the Fourier's law: q = −k∇ x θ, k > 0, (9) with k ∈ C 2 [0, ∞) denoting the heat conductivity coefficient, which depends on the temperature θ in the following way, c 1 1 + θ 3 k(θ) c 2 1 + θ 3 for some c 1 , c 2…”

Stability of weak solutions for the compressible Navier-Stokes-Poisson equations

“…Again, Ducomet [4] showed, by an elementary scaling argument, the global result for the 3-D Navier-Stokes-Poisson system with exterior pressure. Donatelli [8] have proved the global existence of weak solutions of Cauchy problem for the Navier-Stokes-Poisson equation. Zhang & Tan [18] have proved the existence of globally defined finite energy weak solutions of the NavierStokes-Poisson equations for compressible, barotropic flow in two space dimensions by Orlicz space theory.…”