Please recommend some classical books or articles on the local wellposedness 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 EulerPoisson system (Of course, I need to the help of some classical articles). ^^
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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. BenzoniGavage and I: Multidimensional hyperbolic partial differential equations. First order systems and applications. Oxford University Press (2007). 

