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Mathematical Physics Studies

Magnetohydrodynamics: Waves and Shock Waves in Curved Space-Time

Authors: Lichnerowicz, A.

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For seventy years, we have known that Einstein's theory is essentially a theory of propagation of waves for the gravitational field. Confusion enters, however, through the fact that the word wave, in physics, implies sometimes repetition and sometimes not. This confusion is often increased by he use of Fourier transforms, by which a disturbanse which appears to be without repetition is resolved into periodic wave-trains with all frequencies. But, in a general curved space-time, we have nothing corresponding to Fourier transforms. Here, we consider systematically waves corresponding to the propagation of discontinuities of physical quantities describing either fields (essentially electromagnetic fields and gravitational field), or the motion of a fluid, or together, in magnetohydrodynamics, the changes in time of a field and of a fluid. The main equations, for the different studied phenomena, constitute a hyperbolic system and the study of a formal Cauchy problem is possible. We call ordinary waves the case in which the derivative of superior order appearing in the system are discontinuous at the traverse of a hypersurface, the wave front ; we call shock waves the case where the derivatives of an order inferior by one are discontinuous at the traverse of a wave front. XI xii PREFACE From 1950, many well-known scientits (Taub, Synge, Choquet-B ruhat, etc.) have studied the corresponding equations for different physical phenomena : systems associated to the electromagnetic and gravitational fields, to hydrodynamics and to magnetohydrodynamics.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $149.00
price for USA in USD
  • ISBN 978-94-017-2126-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.99
price for USA in USD
Softcover $199.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Magnetohydrodynamics: Waves and Shock Waves in Curved Space-Time
Authors
Series Title
Mathematical Physics Studies
Series Volume
14
Copyright
1994
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-017-2126-4
DOI
10.1007/978-94-017-2126-4
Hardcover ISBN
978-0-7923-2805-6
Softcover ISBN
978-90-481-4390-0
Series ISSN
0921-3767
Edition Number
1
Number of Pages
XII, 280
Topics