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

作者：Xu Jiang^*; Kawashima Shuichi

来源：Journal of Differential Equations, 2013, 256(2): 771-796.

DOI：10.1016/j.jde.2013.09.019

• Compressible Euler equations
• Diffusive relaxation
• Chemin-Lerner spaces

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.

• 出版日期2013-1-15
• 单位南京航空航天大学