Asymptotic behavior of the 3D compressible Euler equations with nonlinear damping and slip boundary condition (Q442971)

Summary: The asymptotic behavior (as well as the global existence) of classical solutions to the 3D compressible Euler equations are considered. For polytropic perfect gas \((P(\rho) = P_0 \rho^\gamma)\), time asymptotically, it has been proved by \textit{R. Pan} and \textit{K. Zhao} [J. Differ. Equations 246, No. 2, 581--596 (2009; Zbl 1155.35066)] 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.