Optimal time decay rates for the compressible Navier-Stokes system with and without Yukawa-type potential
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Date
2020-09-29
Authors
Chen, Qing
Wu, Guochun
Zhang, Yinghui
Zou, Lan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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 L1(ℝ3), 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.
Description
Keywords
Compressible flow, Energy method, Optimal decay rates
Citation
Chen, Q., Wu, G., Zhang, Y., & Zou, L. (2020). Optimal time decay rates for the compressible Navier-Stokes system with and without Yukawa-type potential. <i>Electronic Journal of Differential Equations, 2020</i>(102), pp. 1-25.
Rights
Attribution 4.0 International