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
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.
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
Affiliations des auteurs :
Guochun Wu 1 ; Zhensheng Gao 1
@article{10_4064_ap4020_2_2017,
author = {Guochun Wu and Zhensheng Gao},
title = {Global existence and asymptotic behavior for the full compressible {Euler} equations with damping in $\mathbb R^3$},
journal = {Annales Polonici Mathematici},
pages = {147--163},
publisher = {mathdoc},
volume = {119},
number = {2},
year = {2017},
doi = {10.4064/ap4020-2-2017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap4020-2-2017/}
}
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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
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