Article ID Journal Published Year Pages File Type
4609996 Journal of Differential Equations 2014 26 Pages PDF
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)Hs(Rd)(s>1+d/2)(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.

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Physical Sciences and Engineering Mathematics Analysis
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