Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 771-796 |
| Number of pages | 26 |
| Journal | Journal of Differential Equations |
| Volume | 256 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2014 Jan 15 |
| Externally published | Yes |
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Keywords
- Chemin-Lerner spaces
- Compressible Euler equations
- Diffusive relaxation
ASJC Scopus subject areas
- Analysis
Cite this
Diffusive relaxation limit of classical solutions to the damped compressible Euler equations. / Xu, Jiang; Kawashima, Shuichi.
In: Journal of Differential Equations, Vol. 256, No. 2, 15.01.2014, p. 771-796.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Diffusive relaxation limit of classical solutions to the damped compressible Euler equations
AU - Xu, Jiang
AU - Kawashima, Shuichi
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
UR - http://www.scopus.com/inward/record.url?scp=84886774952&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84886774952&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2013.09.019
DO - 10.1016/j.jde.2013.09.019
M3 - Article
VL - 256
SP - 771
EP - 796
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 2
ER -