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

Abstract

Abstract. In this paper, we consider the global behavior of weak solutions of Navier-Stokes-Poisson equations in time in a bounded domain-arbitrary forces. After proving the existence of bounded absorbing sets, we also obtain the conclusion on asymptotic compactness of global trajectories generated by the Navier-Stokes-Poisson equations of a compressible fluid. Mathematics Subject Classification (2000). 35Q30, 35B41.

A note on global existence of weak solutions to the compressible magnetohydrodynamic equations with Coulomb force

“…We remark that, as for a particular case when magnetic fluid M is absent, above Theorem 2.1 also implies the global existence of the finite energy weak solutions to the Navier-Stokes-Poisson equations in [10][11][12] for two-dimensional case.…”

Global weak solutions to 3D compressible Navier–Stokes–Poisson equations with density-dependent viscosity

“…Cai and Tan [4] also proved the system has the global weak time-periodic solution for the Navier-Stokes-Poisson equations in a bounded domain with periodic boundary condition as γ > 5 3 when the external force is time-periodic. Besides, Jiang et al [16] considered the global behavior of weak solutions of the Navie-Stokes-Poisson equations in a bounded domain with arbitrary forces.…”

Weak time-periodic solutions to the compressible Navier–Stokes–Poisson equations

“…The Navier-Stokes-Poisson equation has been the subject of many studies by physicists and mathematicians because of its physical importance, complexity, rich phenomena, and mathematical challenges; for example, see [2,3,4,5,11,14,19] and the references cited therein. Especially, in Ducomet et al [4,5] proved the existence of global weak solutions of compressible barotropic self-gravitating fluids for the whole and exterior domain case.…”

“…In Kobayashi and Suzuki [14] studied the Navier-Stokes-Poisson Equation (1.1) without the external force, on the fixed bounded domain Ω without radial symmetry or solid core, and show the existence of the weak solution in a reasonable function space including the equilibrium state, emphasizing that the vacuum region {x ∈Ω|ρ(x,t) = 0} can exist inside this domain Ω although the equilibrium state is everywhere positive in this problem. Jiang [11] considers the global behavior of weak solutions of Navier-Stokes-Poisson equations in time in a bounded domain with arbitrary forces. It also should be noted that there are other forms of compressible Navier-Stokes-Poisson system which are slightly different from the system of (1.1) and can be used to simulate, for instance in semiconductor devices, the transport of charged particles under the electric field of electrostatic potential force rather than the Newtonian gravitational potential force.…”

“…Recently, for ferrofluids driven by the time periodic external forces, use the ideas and techniques in [7], Yan [18] showed that such system has the weak time-periodic solutions for γ > 9 5 . In this paper, inspired by [7,8,9,11,14] we will prove the existence of weak timeperiodic solutions to the problem (1.1)-(1.3), that is…”