Post-Newtonian approximation of the Vlasov-Nordström system

Communications in Partial Differential Equations

Volumn 30, Issue 7-9, 2005, Pages 957-985

  Bauer, Sebastian ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

1.5 post Newtonian approximation; Classical limit; Darwin system; Vlasov Nordstr m system

Indexed keywords

EID: 27744530225     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-200064434     Document Type: Article

References (26)

1. Andreasson, H., Calogero, S., Rein, G. (2005). Global classical solutions to the spherically symmetric Nordström-Vlasov system. Math. Proc. Cam. Phil. Soc. 138:533-539.
2. Bauer, S., Kunze, M. (2005). The Darwin approximation of the relativistic Vlasov-Maxwell system. Ann. H. Poincaré 6:283-308. ArXiv preprint math-ph/0401012.
3. Calogero, S., Lee, H. (2004). The non-relativistic limit of the Nordström-Vlasov system. Commun. Math. Sci. 2:19-34.
4. Calogero, S., Rein, G. (2003). On classical solutions of the Nordström-Vlasov system. Comm. Partial Diff. Eqs. 28:1-29.
5. Calogero, S., Rein, G. (2004). Global weak solutions to the Nordström-Vlasov system. Diff. Eqs. 204:323-338.
6. Friedrich, S. (preprint). Global small solutions of the Vlasov-Nordström system. ArXiv preprint math-ph/0404007.
7. Glassey, R. T. (1996). The Cauchy Problem in Kinetic Theory. Philadelphia: SIAM.
8. Glassey, R. T., Strauss, W. (1986). Singularity formation in a collisionless plasma could occur only at high velocities. Arch. Rational Mech. Anal. 92:59-90.
9. Horst, E. (1993). On the asymptotic growth of the solutions of the Vlasov-Poisson system. Math. Methods Appl. Sci. 16:75-85.
10. Kunze, M., Rendall, A. D. (2001). The Vlasov-Poisson system with radiation damping. Ann. H. Poincaré 2:857-886.
11. Kunze, M., Rendall, A. D. (2001). Simplified models of electromagnetic and gravitational radiation damping. Classical Quantum Gravity 18:3573-3587.
12. Kunze, M., Spohn, H. (2000). Slow motion of charges interacting through the Maxwell field. Comm. Math. Phys. 212:437-467.
13. -3. J. Nonlinear Sci. 11:321-396.
14. Lee, H. (2004). The classical limit of the relativistic Vlasov-Maxwell system in two space dimensions. Math. Methods Appl. Sci. 27:249-287.
15. Lee, H. (preprint). Global existence of solutions of the Nordström-Vlasov system in two space dimensions. ArXiv preprint math-ph/0312014.
16. k-Regularität der Lösungen des Vlasov-Poisson-Systems Partieller Differentialgleichungen. Diploma Thesis, LMU München.
17. Lions, P.-L., Perthame, B. (1991). Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system. Invent. Math. 105:415-430.
18. McOwen, R. C. (1979). The behavior of the Laplacian on weighted Sobolev spaces. Comm. Pure Appl. Math. 32:783-795.
19. Nordström, G. (1913). Zur Theorie der Gravitation vom Standpunkt des Relativitätsprinzip. Ann. Phys. Lpz. 42:533.
20. Pfaffelmoser, K. (1992). Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data. J. Diff. Eqs. 95:281-303.
21. Rein, G. (1997). Selfgravitating systems in Newtonian theory-the Vlasov-Poisson system. In Proc. Minisemester on Math. Aspects of Theories of Gravitation 1996. Banach Center Publications 41, Part I, pp. 179-194.
22. Rendall, A. D. (1994). The Newtonian limit for asymptotically flat solutions of the Vlasov-Einstein system. Comm. Math. Phys. 163:89-112.
23. Schaeffer, J. (1986). The classical limit of the relativistic Vlasov-Maxwell system. Comm. Math. Phys. 104:403-421.
24. Schaeffer, J. (1991). Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions. Comm. Partial Diff. Eqs. 16:1313-1335.
25. Shapiro, S. L., Teukolsky, S. A. (1993). Scalar gravitation: a laboratory for numerical relativity. Phys. Rev. 47:1529-1540.
26. Spohn, H. (2004). Dynamics of Charged Particles and their Radiation Field. Cambridge: Cambridge Univ. Press.