Journal of Applied Mathematics
Volume 2012 (2012), Article ID 584680, 16 pages
Research Article

Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition

Department of Mathematics, Shandong Normal University, Jinan 250014, China

Received 7 January 2012; Accepted 1 March 2012

Academic Editor: Laurent Gosse

Copyright © 2012 Huimin Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The asymptotic behavior (as well as the global existence) of classical solutions to the 3D compressible Euler equations are considered. For polytropic perfect gas ( 𝑃 ( 𝜌 ) = 𝑃 0 𝜌 𝛾 ) , time asymptotically, it has been proved by Pan and Zhao (2009) that linear damping and slip boundary effect make the density satisfying the porous medium equation and the momentum obeying the classical Darcy's law. In this paper, we use a more general method and extend this result to the 3D compressible Euler equations with nonlinear damping and a more general pressure term. Comparing with linear damping, nonlinear damping can be ignored under small initial data.