Communications in Mathematical Sciences

Volume 15 (2017)

Number 3

Time periodic solutions to the compressible Navier–Stokes–Poisson system with damping

Pages: 789 – 812



Hong Cai (School of Mathematical Sciences, Xiamen University, Fujian, Xiamen, China)

Zhong Tan (School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing, Xiamen University, Fujian, Xiamen, China)


In this paper, we establish the existence of time periodic solutions to the two and three dimensional compressible Navier–Stokes–Poisson equations with the linear damping, under some smallness and symmetry assumptions on the time periodic external force. Based on the uniform estimates and the topological degree theory, we prove the existence of a time periodic solution in a bounded domain. Finally, the existence result in the whole space is obtained by a limiting process.


Navier–Stokes–Poisson equations, time periodic solution, uniform estimates, topological degree theory

2010 Mathematics Subject Classification

35B10, 35M10, 35Q35

Published 24 February 2017