Geodesic
Global existence and asymptotic behavior for the full compressible Euler equations with damping in $\mathbb R^3$
Guochun Wu1 ; Zhensheng Gao1
1 School of Mathematical Sciences Huaqiao University Quanzhou 362021, China
Annales Polonici Mathematici, Tome 119 (2017) no. 2, pp. 147-163.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We are concerned with the global existence and asymptotic behavior of classical solutions to the Cauchy problem for the full compressible Euler equations with damping in $\mathbb R^3$. We prove the global existence of the classical solutions by the delicate energy method under the condition that the initial data are close to the constant equilibrium state in $H^3$-framework. An energy estimate on $\| \nabla u\| _{L^1((0,t);\tilde{B}^{0,{3/2}}_{2,1}(\mathbb R^3))}$ enables us to close the energy estimates for the non-dissipative entropy. Moreover, the optimal time decay rate is also established.
DOI : 10.4064/ap4020-2-2017
Keywords: concerned global existence asymptotic behavior classical solutions cauchy problem full compressible euler equations damping mathbb prove global existence classical solutions delicate energy method under condition initial close constant equilibrium state framework energy estimate nabla tilde mathbb enables close energy estimates non dissipative entropy moreover optimal time decay rate established

Guochun Wu 1 ; Zhensheng Gao 1

1 School of Mathematical Sciences Huaqiao University Quanzhou 362021, China 
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     title = {Global existence and asymptotic behavior for the full compressible {Euler} equations with damping in $\mathbb R^3$},
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Guochun Wu; Zhensheng Gao. Global existence and asymptotic behavior for the full compressible Euler equations with damping in $\mathbb R^3$. Annales Polonici Mathematici, Tome 119 (2017) no. 2, pp. 147-163. doi : 10.4064/ap4020-2-2017. http://geodesic.mathdoc.fr/articles/10.4064/ap4020-2-2017/

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