TY - JOUR
T1 - Diffusive relaxation limit of classical solutions to the damped compressible Euler equations
AU - Xu, Jiang
AU - Kawashima, Shuichi
N1 - Funding Information:
The authors would like to thank the referee for various comments which improve the presentation of the manuscript. J. Xu is partially supported by the NSFC ( 11001127 ), the Special Foundation of China Postdoctoral Science Foundation ( 2012T50466 ), China Postdoctoral Science Foundation ( 20110490134 ), Postdoctoral Science Foundation of Jiangsu Province ( 1102057C ) and the NUAA Fundamental Research Funds ( NS2013076 ). S. Kawashima is partially supported by Grant-in-Aid for Scientific Research (A) 22244009 .
PY - 2014/1/15
Y1 - 2014/1/15
N2 - We construct (uniform) global classical solutions to the damped compressible Euler equations on the framework of general Besov spaces which includes both the usual Sobolev spaces Hs(Rd) (s>1+d/2) and the critical Besov space B2,11+d/2(Rd). Such extension heavily depends on a revision of commutator estimates and an elementary fact that indicates the connection between homogeneous and inhomogeneous Chemin-Lerner spaces. Furthermore, we obtain the diffusive relaxation limit of Euler equations towards the porous medium equation, by means of Aubin-Lions compactness argument.
AB - We construct (uniform) global classical solutions to the damped compressible Euler equations on the framework of general Besov spaces which includes both the usual Sobolev spaces Hs(Rd) (s>1+d/2) and the critical Besov space B2,11+d/2(Rd). Such extension heavily depends on a revision of commutator estimates and an elementary fact that indicates the connection between homogeneous and inhomogeneous Chemin-Lerner spaces. Furthermore, we obtain the diffusive relaxation limit of Euler equations towards the porous medium equation, by means of Aubin-Lions compactness argument.
KW - Chemin-Lerner spaces
KW - Compressible Euler equations
KW - Diffusive relaxation
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U2 - 10.1016/j.jde.2013.09.019
DO - 10.1016/j.jde.2013.09.019
M3 - Article
AN - SCOPUS:84886774952
VL - 256
SP - 771
EP - 796
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 2
ER -