Optimal time decay rates for the compressible Navier-Stokes system with and without Yukawa-type potential

• Main Authors: Qing Chen, Guochun Wu, Yinghui Zhang, Lan Zou
• Format: Article
• Language: English
• Published: Texas State University 2020-09-01
• Series: Electronic Journal of Differential Equations
• Subjects: compressible flow; energy method; optimal decay rates
• Online Access: http://ejde.math.txstate.edu/Volumes/2020/102/abstr.html
• ISSN: 1072-6691

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.