Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition
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)=P0ργ), time asymptotically, it has been proved by Pan and Zhao (2009) that linear damping and slip boundary effect make the density...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/584680 |
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| author | Huimin Yu |
| author_facet | Huimin Yu |
| author_sort | Huimin Yu |
| collection | DOAJ |
| description | 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)=P0ργ), 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. |
| format | Article |
| id | doaj-art-6a398e89f36b4aa091f4fdc21640d830 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6a398e89f36b4aa091f4fdc21640d8302025-02-03T01:27:50ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/584680584680Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary ConditionHuimin Yu0Department of Mathematics, Shandong Normal University, Jinan 250014, ChinaThe 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)=P0ργ), 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.http://dx.doi.org/10.1155/2012/584680 |
| spellingShingle | Huimin Yu Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition Journal of Applied Mathematics |
| title | Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition |
| title_full | Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition |
| title_fullStr | Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition |
| title_full_unstemmed | Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition |
| title_short | Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition |
| title_sort | asymptotic behavior of the 3d compressible euler equations with nonlinear damping and slip boundary condition |
| url | http://dx.doi.org/10.1155/2012/584680 |
| work_keys_str_mv | AT huiminyu asymptoticbehaviorofthe3dcompressibleeulerequationswithnonlineardampingandslipboundarycondition |