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Euler equations and related hyperbolic conservation laws. (English) Zbl 1092.35062
Dafermos, C.M.(ed.) et al., Evolutionary equations. Vol. II. Amsterdam: Elsevier/North-Holland (ISBN 0-444-52048-1/hbk). Handbook of Differential Equations, 1-104 (2005).
Some basic features of Euler equations such as convex entropy, hyperbolicity, genuine nonlinearity, singularities and BV bounds and the associated conservation laws are reviewed along with the description of some aspects of well-posedness and related results. Some analytical approaches including techniques for analysing multidimensional models are presented. Also some recent results, concerning divergence-measure fields, to construct a global framework for studying solutions of multidimensional flows and hyperbolic system of conservation laws are discussed. It is a well written review article which should be of interest to some-one working on hyperbolic conservation laws.
For the entire collection see [Zbl 1074.35003].

35L65 Hyperbolic conservation laws
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35Q35 PDEs in connection with fluid mechanics