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Please recommend some classical books or articles on the local well-posedness result of compressible Euler equations ! The main aim is that I want to learn some basic methods and techniques about the local existence theory of quasilinear hyperbolic system. Eventually, I can apply the tools I mastered to solve the Euler-Poisson system (Of course, I need to the help of some classical articles). ^-^

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up vote 4 down vote accepted

By far, the ever best written book on the subject is that of Constantin Dafermos: Hyperbolic Conservation Law in Continuum Physics. Grundlehren der Mathematischen Wissenschaften 325, Springer Verlag.

Edit. Of course, if you are already a bit familiar with the topic, you may have a look to the book by S. Benzoni-Gavage and I: Multi-dimensional hyperbolic partial differential equations. First order systems and applications. Oxford University Press (2007).

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@Denis Serre: Thank you very much! :-) –  Darry Dec 3 '12 at 14:43
    
I am reading Benzon-Gavage and Serre. I have not reached the Euler stuff yet but the book is superb! –  timur Apr 19 '13 at 13:52
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