Diffusive relaxation limit of classical solutions to the damped compressible Euler equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Xu, Jiang¹  Kawashima, Shuichi² 

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Jiangsu, Peoples R China

[2] Kyushu Univ, Grad Sch Math, Fukuoka 8128581, Japan

关键词: Compressible Euler equations;    Diffusive relaxation;    Chemin-Lerner spaces;   

DOI  :  10.1016/j.jde.2013.09.019

来源: Elsevier

【 摘 要 】

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 H-s (R-d) (s > 1 + d/2) and the critical Besov space B-2,1(1+d/2) (R-d). 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free