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

[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.

[学科分类] 数学（综合）

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