The Newtonian limit for perfect fluids

Communications in Mathematical Physics

Volumn 276, Issue 1, 2007, Pages 131-188

  Oliynyk, Todd A ^a,b  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b MONASH UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34848849454     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0334-z     Document Type: Article

References (41)

1. Bartnik R. (1986). The Mass of an Asymptotically Flat Manifold. Comm. Pure Appl. Math. 39: 661-693
2. Blanchet L. and Damour T. (1986). Radiative gravitational fields in general relativity. I. General structure of the field outside the source. Phil. Trans. Roy. Soc. Lond. A 320: 379-430
3. Blanchet L., Faye G. and Nissanke S. (2005). On the structure of the post-Newtonian expansion in general relativity. Phys. Rev. D 72: 44024
4. Brauer, U., Karp, L.: Local existence of classical solutions for the Einstein-Euler system using weighted Sobolev spaces of fractional order. Preprint, available at http://www.math.uni-potsdam.de/prof/a_partdiff/prep/ 2006_17.pdf, 2006
5. Browning G. and Kreiss H.O. (1982). Problems with different time scales for nonlinear partial differential equations. SIAM J. Appl. Math. 42: 704-718
6. Chandrasekhar S. (1965). The post-Newtonian equations of hydrodynamics in general relativity. Ap. J. 142: 1488-1512
7. s,δ spaces on manifolds which are Euclidean at infinity. Acta. Math. 146: 129-150
8. Chruściel P.T. and Delay E. (2003). On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications. Mem. Soc. Math. France 94: 1-103
9. Dautcourt G. (1964). Die Newtonsche Gravitationstheorie als strenger Grenzfall der Allgemeinen Relativitätstheorie. Acta Phys. Polonica 25: 637-646
10. Deimling K. (1998). Nonlinear functional analysis. Springer-Verlag, Berlin
11. Duval C., Burdet G., Künzle H.P. and Perrin M. (1985). Bargmann structures and Newton-Cartan theory. Phys. Rev. D. 31: 1841-1853
12. Ehlers, J.: On limit relations between, and approximative explanations of, physical theories. In: R. Barcan Marcus, G.J.W. Dorn, P. Weingartner, Logic, methodology and philosophy of science VII, Amsterdam: North Holland, 1986, pp. 387-403
13. Einstein A., Infeld L. and Hoffmann B. (1938). The gravitational equations and the problem of motion. Ann. Math. 39: 65-100
14. Frauendiener J. (2003). A note on the relativistic Euler equations. Class. Quantum Grav. 20: L193-196
15. Friedrich H. (1998). Evolution equations for gravitating ideal fluid bodies in general relativity. Phys. Rev. D 57: 2317-2322
16. Frittelli S. and Reula O. (1994). On the Newtonian limit of general relativity. Commun. Math. Phys. 166: 221-235
17. Heilig U. (1995). On the Existence of Rotating Stars in General Relativity. Commun. Math. Phys. 166: 457-493
18. Iriondo M.S., Mirta S., Leguizamón E.O. and Reula O.A. (1998). Fast and slow solutions in general relativity: the initialization procedure. J. Math. Phys. 39: 1555-1565
19. Klainerman S. and Majda A. (1982). Compressible and incompressible fluids. Comm. Pure Appl. Math. 35: 629-651
20. Künzle H.P. (1972). Galilei and Lorentz structures on space-time: comparison of the corresponding geometry and physics. Ann. Inst. Henri Poincaré 17: 337-362
21. Künzle H.P. (1976). Covariant Newtonian limit of Lorentz space-times. Gen. Rel. Grav. 7: 445-457
22. Künzle H.P. and Duval C. (1986). Relativistic and non-relativistic classical field theory on five-dimensional spacetime. Class. Quantum Grav. 3: 957-974
23. Lottermoser M. (1992). A convergent post-Newtonian approximation for the constraints in general relativity. Ann. Inst. Henri Poincaré 57: 279-317
24. Makino, T.: On a local existence theorem for the evolution equation of gaseous stars. In: Patterns and Waves, edited by T. Nishida, M. Mimura, H. Fujii, Amsterdam: North-Holland, 1986
25. Maxwell, D.: Rough solutions of the Einstein constraint equations. Preprint, available at http://arxiv.org/ list/gr-qc/0405088, 2004
26. Noundjeu, P.: On the non-relativistic limit of the spherically symmetric Einstein-Vlasov-Maxwell system. Preprint available at http://arxiv.org/list/gr- qc/0508078, 2005
27. Oliynyk, T.A.: Post-Newtonian expansions for perfect fluids. In preparation.
28. Oliynyk T.A. (2005). Newtonian perturbations and the Einstein-Yang-Mills- dilaton equations. Class. Quantum Grav. 22: 2269-2294
29. Oliynyk T.A. (2006). An existence proof for the gravitating BPS monopole. Inst. Henri Poincaré 7: 199-232
30. Oliynyk, T.A., Woolgar, E.: Asymptotically flat Ricci flows. Preprint, available at http://arxiv.org/list/ math/0607438, 2006
31. Pati M.E. and Will C.M. (2000). Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations: foundations. Phys. Rev. D 62: 124015
32. Rein G. and Rendall A.D. (1992). The Newtonian limit of the spherically symmetric Vlasov-Einstein system. Commun. Math. Phys. 150: 585-591
33. Rendall A.D. (1990). Convergent and divergent perturbation series and the post-Minkowskian approximation scheme. Class. Quantum Grav. 7: 803-812
34. Rendall A.D. (1992). The initial value problem for a class of general relativistic fluid bodies. J. Math. Phys. 33: 1047-1053
35. Rendall A.D. (1992). On the definition of post-Newtonian approximations. Proc. R. Soc. Lond. A 438: 341-360
36. Rendall A.D. (1994). The Newtonian limit for asymptotically flat solutions of the Vlasov-Einstein system. Comm. Math. Phys. 163: 89-112
37. Schochet S. (1986). Symmetric hyperbolic systems with a large parameter. Comm. partial differential equations 11: 1627-1651
38. Schochet S. (1988). Asymptotics for symmetric hyperbolic systems with a large parameter. J. differential equations 75: 1-27
39. Taylor M.E. (1996). Partial differential equations III, nonlinear equations. Springer, New York
40. Walton R.A. (2005). A symmetric hyperbolic structure for isentropic relativistic perfect fluids. Houston J. Math. 31: 145-160
41. Will C.M. (2005). Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. III. Radiation reaction for binary systems with spinning bodies. Phys. Rev. D 71: 084027