Communications in Mathematical Sciences

Volume 19 (2021)

Number 8

Stationary solutions of outflow problem for full compressible Navier–Stokes–Poisson system: existence, stability and convergence rate

Pages: 2195 – 2215



Hakho Hong (Institute of Mathematics, State Academy of Sciences, Pyongyang, North Korea)

Jongsung Kim (School of Mathematics, Pyongyang University of Mechanical Engineering, Pyongyang, North Korea)

Kwang-Il Choe (School of Mathematics, Pyongyang University Of Mechanical Engineering, Pyongyang, North Korea)


In this paper, we study the asymptotic behavior of solution to the initial boundary value problem for the non-isentropic Navier–Stokes–Poisson system in a half line $(0,\infty)$. We consider an outflow problem where the gas blows out the region through the boundary for general gases including ideal polytropic gas. First, we give necessary condition for the existence of stationary solution by use of the center manifold theory. Second, using energy method we show the asymptotic stability of the solutions under assumptions that the boundary value and the initial perturbation is small. Third, we prove that the algebraic and exponential decay of the solution toward supersonic stationary solution is obtained, when the initial perturbation belongs to Sobolev space with algebraic and exponential weight respectively.


Navier–Stokes–Poisson equations, outflow problem, stationary solution, stability, convergence rate

2010 Mathematics Subject Classification

34K21, 39A30, 41A25, 76N10, 76N99

Received 9 December 2020

Accepted 10 May 2021

Published 7 October 2021