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**Relativistic fluids and magneto-fluids. With applications in astrophysics and plasma physics.**
*(English)*
Zbl 0701.76003

Cambridge Monographs on Mathematical Physics. Cambridge etc.: Cambridge University Press. ix, 336 p. £50.00; $ 85.00 (1989).

Since 1967, the publication of A. Lichnerowicz’s monograph on “Relativistic hydrodynamics and magnetohydrodynamics” (Zbl 0193.554) which offered a modern treatment of existence and uniqueness theorems in the frame of the results in general relativity obtained mainly by the French school, no attempt has appeared to study comprehensively the newer results. However, the pression of the experimental facts, due to the achievements of observational astronomy and astrophysics, catalyzed pioneer studies of the subject in connection with supernova explosion, jets in extragalactic radio sources, accretion onto neutron stars, and black holes and even in down to earth physics of energetic particle beams and nuclear reactions. Author gives here a survey of some of the theoretical methods used to describe the relativistic fluid models of relevance to astrophysical, nuclear and plasma physical applications. The attention is concentrated on the nonlinear wave problem.

The book, which refers to more than 200 contributions in the bibliography, and among them 23 are those of the authors, is devided into 10 chapters. The first introduces the mathematical formalism to be used, shown on the relativistic fluids in question. The second treats singular hypersurfaces in space-time. The third is devoted to the propagation of weak discontinuities. The fourth deals with the relativistic simple waves. The sixth summarizes the relativistic geometrical optics /the ray problem/. Then the seventh reviews the relativistic asymptotic waves. The eighth treats the relativistic shock waves, the ninth their propagation and the tenth their stability. The virtue of the book - besides the original contributions of the author - is the concise and comprehensive treatment of the phenomena in the field with an interest in the recently actual physical investigations.

The book, which refers to more than 200 contributions in the bibliography, and among them 23 are those of the authors, is devided into 10 chapters. The first introduces the mathematical formalism to be used, shown on the relativistic fluids in question. The second treats singular hypersurfaces in space-time. The third is devoted to the propagation of weak discontinuities. The fourth deals with the relativistic simple waves. The sixth summarizes the relativistic geometrical optics /the ray problem/. Then the seventh reviews the relativistic asymptotic waves. The eighth treats the relativistic shock waves, the ninth their propagation and the tenth their stability. The virtue of the book - besides the original contributions of the author - is the concise and comprehensive treatment of the phenomena in the field with an interest in the recently actual physical investigations.

Reviewer: I.Abonyi

### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |