an:07261909
Zbl 1444.35123
Chen, Qing; Wu, Guochun; Zhang, Yinghui; Zou, Lan
Optimal time decay rates for the compressible Navier-Stokes system with and without Yukawa-type potential
EN
Electron. J. Differ. Equ. 2020, Paper No. 102, 25 p. (2020).
00444513
2020
j
35Q30 76N15
compressible flow; energy method; optimal decay rates
Summary: We consider the time decay rates of smooth solutions to the Cauchy problem for the compressible Navier-Stokes system with and without a Yukawa-type potential. We prove the existence and uniqueness of global solutions by the standard energy method under small initial data assumptions. Furthermore, if the initial data belong to \(L^1(\mathbb{R}^3)\), we establish the optimal time decay rates of the solution as well as its higher-order spatial derivatives. In particular, we obtain the optimal decay rates of the highest-order spatial derivatives of the velocity. Finally, we derive the lower bound time decay rates for the solution and its spacial derivatives.