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 - Jan 15 2014 |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
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Xu, J., & Kawashima, S. (2014). Diffusive relaxation limit of classical solutions to the damped compressible Euler equations. Journal of Differential Equations, 256(2), 771-796. https://doi.org/10.1016/j.jde.2013.09.019