Electron. J. Differential Equations,
Vol. 2019 (2019), No. 61, pp. 118.
Decay rate of strong solutions to compressible NavierStokesPoisson equations
with external force
Yeping Li, Nengqiu Zhang
Abstract:
In this article, we consider the three dimensional compressible
NavierStokesPoisson equations with the effect of external
potential force. First, the stationary solution is established by
solving a nonlinear elliptic system. Next, we show global wellposedness
of the strong solutions for the initial value problem to the three
dimensional compressible NavierStokesPoisson equations when the
initial data are close to the stationary solution in
.
Moreover, if the
norm of initial perturbation is finite,
we prove the optimal
decay rates for such
strong solution and
decay rate of its firstorder
spatial derivatives via a low frequency and high frequency decomposition.
Submitted October 7, 2018. Published May 7, 2019.
Math Subject Classifications: 35M20, 35Q35, 76W05.
Key Words: NavierStokesPoisson equation; stationary solution;
strong solution; energy estimate; optimal decay rate.
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Yeping Li
Department of Mathematics
East China University of Science and Technology
Shanghai 200237, China
email: yplee@ecust.edu.cn


Nengqiu Zhang
Department of Mathematics
East China University of Science and Technology
Shanghai 200237, China
email: 731835397@qq.com

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