Optimal decay rates for higher-order derivatives of solutions to 3D compressible Navier-Stokes-Poisson equations with external force

Electronic Journal of Differential Equations

article

Liuna Qin¹  Changguo Xiao¹  Yinghui Zhang¹ 

[1] School of Mathematics and Statistics Guangxi Normal University Guilin

关键词: Compressible Navier-Stokes-Poisson system;    external force;    higher-order derivative.;   

DOI  :  10.58997/ejde.2022.64

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

We investigate optimal decay rates for higher-order spatial derivatives of solutions to the 3D compressibleNavier-Stokes-Poisson equations with external force. The main novelty of this article is twofold: First, we prove the first and second order spatial derivatives of the solutions converge to zero at the L2-rate (1+t)-5/4, which is faster than the L2-rate (1+t)-3/4 in Li-Zhang [15]. Second, for well-chosen initial data, we show the lower optimal decay rates of the first order spatial derivative of the solutions. Therefore, our decay rates are optimal in this sense.

【 授权许可】

CC BY