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**Asymptotic behavior of the 3D compressible Euler equations with nonlinear damping and slip boundary condition.**
*(English)*
Zbl 1244.76112

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 R. Pan and 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.

### MSC:

76S05 | Flows in porous media; filtration; seepage |

35Q31 | Euler equations |

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |

### Citations:

Zbl 1155.35066
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\textit{H. Yu}, J. Appl. Math. 2012, Article ID 584680, 16 p. (2012; Zbl 1244.76112)

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### References:

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