Asymptotic behavior of the 3D compressible Euler equations with nonlinear damping and slip boundary condition
type: Item
instance of: scholarly article
title: Asymptotic behavior of the 3D compressible Euler equations with nonlinear damping and slip boundary condition
zbMATH Open document ID: 1244.76112
DOI: 10.1155/2012/584680
author: Huimin Yu
published in: Journal of Applied Mathematics
publication date: 2012-08-06T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 35Q31
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 6063426
Wikidata QID: Q58906183
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/584680
OpenAlex ID: W2025396076
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DBLP publication ID: journals/jam/Yu12a
description: scientific article; zbMATH DE number 6063426