Electron. J. Differential Equations, Vol. 2019 (2019), No. 61, pp. 1-18.

Decay rate of strong solutions to compressible Navier-Stokes-Poisson equations with external force

Yeping Li, Nengqiu Zhang

Abstract:
In this article, we consider the three dimensional compressible Navier-Stokes-Poisson equations with the effect of external potential force. First, the stationary solution is established by solving a nonlinear elliptic system. Next, we show global well-posedness of the strong solutions for the initial value problem to the three dimensional compressible Navier-Stokes-Poisson equations when the initial data are close to the stationary solution in $H^2(\mathbb{R}^3)$. Moreover, if the $L^1(\mathbb{R}^3)$-norm of initial perturbation is finite, we prove the optimal $L^p(\mathbb{R}^3)$ $(2\leq p\leq6)$ decay rates for such strong solution and $L^2(\mathbb{R}^3)$ decay rate of its first-order 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: Navier-Stokes-Poisson 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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