Download Relativistic Fluid Dynamics by Pham Mau Quan (auth.), C. Cattaneo (eds.) PDF

By Pham Mau Quan (auth.), C. Cattaneo (eds.)

Pham Mau Quam: Problèmes mathématiques en hydrodynamique relativiste.- A. Lichnerowicz: Ondes de choc, ondes infinitésimales et rayons en hydrodynamique et magnétohydrodynamique relativistes.- A.H. Taub: Variational ideas commonly relativity.- J. Ehlers: basic relativistic kinetic thought of gases.- ok. Marathe: summary Minkowski areas as fibre bundles.- G. Boillat: Sur l. a. propagation de l. a. chaleur en relativité.

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Relativistic Fluid Dynamics

Pham Mau Quam: Problèmes mathématiques en hydrodynamique relativiste. - A. Lichnerowicz: Ondes de choc, ondes infinitésimales et rayons en hydrodynamique et magnétohydrodynamique relativistes. - A. H. Taub: Variational ideas mostly relativity. - J. Ehlers: common relativistic kinetic thought of gases.

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Example text

X x Le cOne C- (A) x dual de n r x-(A) est defini. de ma- niere analogue. SoH Cx (A) (1. 3) Un chemin r: [0,1] .... Vn temps relativement de r est dans a A + C (A) x U Cx- (A) differentiable est dit oriente dans Ie si la demi-tangente positive en chaque points C:(A). Une hypersurface differentiable r; est dite orien - 32 - Pham tee dans I 'espace relativement gent en chaq~e point T (E) x a A si Ie sous expace vectoriel tan x de 1: est exterieur Definition 3. - On dit que I 'operateur hyperbolique dans tin domaine n C Vn A(x, D) a CIA).

Nous supposons de plus que les donnees d~ Cauchy 1) (gtA~, 0, g •• ' S) sur la forme quadratique gel~ x· X. 1. satisfont aux conditions: est hyperbolique nor-male - 52 - Pham 2) sur Z on a F' = 0 , S'" nit une valeur admissible de = XT·. f ; la seconde relation defi 11 ~ 1. telle que r . tr f (ai). 0 1 et par correspond Ie cOne uti. 12) qui a un interieur non vide. ) 1 est x. Comme il est differentiable , il est strictement hyperbolique dans un voisinage ouvert con- - 53 - Ph am U de nexe x. L 'hypersurface initiale dans I' espace relativement sur t a A, il reste des derivees d'indices 0 de !

X" x,.. J dx~ me parametre. " II. (I f [ u 'd. u~ - (g, - u u~ 'atl/ ] - 59 - Pham On obtient ainsi Ia formule ~S (3. 5) =(W, ~x>~ 4 qui donne Ia variation de I'integrale (3. 6) pour des extremites non fixes. Si Ies variations sont a extremites fixes, bxo = bx~ 0, il vient P 0, c 'est-a-di (3 7\ Pour que S est extremum, il faut et il suffit que re equat ions formellement identiques a (1. 1). D 'ou Theoreme. 6) pour des variations a extremi- tes fixes. 8) g f2 g . 9) Ces extre::nales sont des geodesiques de (V 4' g ).

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