Optimal time-decay rates of the compressible Navier–Stokes–Poisson system in $ \mathbb R^3 $

Guochun Wu; Han Wang; Yinghui Zhang; Guochun Wu; Han Wang; Yinghui Zhang

doi:10.3934/era.2021067

Electronic Research Archive

2021, Volume 29, Issue 6: 3889-3908. doi: 10.3934/era.2021067

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Optimal time-decay rates of the compressible Navier–Stokes–Poisson system in $ \mathbb R^3 $

Guochun Wu ^{1
,},
Han Wang ^{2
,},
Yinghui Zhang ^{2
,
,}

1.
Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
2.
School of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi 541004, China

Received: 01 June 2021 Revised: 01 July 2021 Published: 07 September 2021
35B40, 76N10

We are concerned with the Cauchy problem of the 3D compressible Navier–Stokes–Poisson system. Compared to the previous related works, the main purpose of this paper is two–fold: First, we prove the optimal decay rates of the higher spatial derivatives of the solution. Second, we investigate the influences of the electric field on the qualitative behaviors of solution. More precisely, we show that the density and high frequency part of the momentum of the compressible Navier–Stokes–Poisson system have the same $ L^2 $ decay rates as the compressible Navier–Stokes equation and heat equation, but the $ L^2 $ decay rate of the momentum is slower due to the effect of the electric field.
- Navier–Stokes–Poisson equations,
- large time behavior,
- optimal decay rates
Citation: Guochun Wu, Han Wang, Yinghui Zhang. Optimal time-decay rates of the compressible Navier–Stokes–Poisson system in $ \mathbb R^3 $[J]. Electronic Research Archive, 2021, 29(6): 3889-3908. doi: 10.3934/era.2021067

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Abstract

We are concerned with the Cauchy problem of the 3D compressible Navier–Stokes–Poisson system. Compared to the previous related works, the main purpose of this paper is two–fold: First, we prove the optimal decay rates of the higher spatial derivatives of the solution. Second, we investigate the influences of the electric field on the qualitative behaviors of solution. More precisely, we show that the density and high frequency part of the momentum of the compressible Navier–Stokes–Poisson system have the same $ L^2 $ decay rates as the compressible Navier–Stokes equation and heat equation, but the $ L^2 $ decay rate of the momentum is slower due to the effect of the electric field.

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