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

Abstract

In this paper, we consider the isentropic compressible Navier-Stokes-Poisson equations arising from transport of charged particles or motion of gaseous stars in astrophysics. We are interested in the case that the viscosity coefficients depend on the density and shall degenerate in the appearance of (density) vacuum, and show the L 1 -stability of weak solutions for arbitrarily large data on spatial multi-dimensional bounded or periodic domain or whole space.

Global Existence of Solution to Initial Boundary Value Problem for Bipolar Navier-Stokes-Poisson System

“…The quasineutral and some related asymptotic limits were studied in [3][4][5]. In the case when the Poisson equation describes the self-gravitational force for stellar gases, the global existence of weak solution and asymptotic behavior were also investigated together with the stability analysis; refer to [6,7] and the references therein. In addition, Hao and Li [8] proved the global well-posedness of NSP in the Besov space.…”