Effective dynamics for boson stars

Nonlinearity

Volumn 20, Issue 5, 2007, Pages 1031-1075

  Frohlich J ^a   Jonsson, B L G ^b   Lenzmann, E ^c  

^a ETH ZURICH   (Switzerland)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34249294052     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/20/5/001     Document Type: Article

References (35)

1. Elgart A and Schlein B 2007 Mean field dynamics of boson stars Commun. Pure Appl. Math. 60 500-45
2. Fröhlich J, Jonsson B L G and Lenzmann E 2007 Boson stars as solitary waves Commun. Math. Phys. at press (Preprint math-ph/0512040)
3. Lenzmann E 2006 Well-posedness for semi-relativistic Hartree equations of critical type Math. Phys. Anal. Geom. at press (Preprint math.AP/0505456)
4. Cho Y and Ozawa T 2006 On the semirelativistic Hartree-type equation SIAM J. Math. Anal. 38 1060-74
5. Fröhlich J and Lenzmann E 2006 Blow-up for nonlinear wave equations describing boson stars Commun. Pure Appl. Math. at press (Preprint math.AP/0511003)
6. Cazenave T and Lions P-L 1982 Orbital stability of standing waves for some nonlinear Schrödinger equations Commun. Math. Phys. 85 549-61
7. Ruffini R and Bonazzola S 1969 Systems of self-graviting particles in general relativity and the concept of an equation of state Phys. Rev. II 187 1767-83
8. 2/r Commun. Math. Phys. 53 285-94
9. Weder R 1974 Spectral properties of one-body relativistic spin-zero Hamiltonians Ann. Inst. H Poincaré A 20 211-20
10. Messer J 1981 Temperature Dependent Thomas-Fermi Theory (Lecture Notes in Physics) vol 147 (Berlin: Springer)
11. Thirring W 1983 Bosonic black holes Phys. Lett. B 127 27-9
12. Lieb E H and Thirring W E 1984 Gravitational collapse in quantum mechanics with relativistic kinetic energy Ann. Phys., NY 155 494-512
13. Lieb E H and Yau H-T 1987 The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics Commun. Math. Phys. 112 147-74
14. Fröhlich J and Lenzmann E 2004 Mean-field limit of quantum Bose gases and nonlinear Hartree equation Sémin. qu. Dériv. Partielles. (2003-2004) (Palaiseau: cole Polytech.) pp XIX1-26 (Preprint math-ph/0409019)
15. Weinstein M I 1985 Modulational stability of ground states of nonlinear Schrödinger equations SIAM J. Math. Anal. 16 472-91
16. Weinstein M I 1986 Lyapunov stability of ground states of nonlinear dispersive evolution equations Commun. Pure Appl. Math. 39 51-68
17. Stuart D M A 2001 Modulational approach to stability of non-topological solitons in semilinear wave equations J. Math. Pure. Appl. 80 51-83
18. 1 of the sum of k solitary waves for some nonlinear Schrödinger equations Duke Math. J. 133 405-66
19. Perelman G 2004 Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations Commun. Partial Diff. Eqns 29 1051-95
20. Rodnianski I, Schlag W and Soffer A 2003 Asymptotic stability of n-soliton states of NLS Preprint math.AP/0309114
21. Bronski J C and Jerrard R L 2000 Soliton dynamics in a potential Math. Res. Lett. 7 329-42
22. Fröhlich J, Tsai T-P and Yau H-T 2002 On the point-particle (Newtonian) limit of the non-linear Hartree equation Commun. Math. Phys. 225 223-74
23. Fröhlich J, Gustafson S, Jonsson B L G and Sigal I M 2004 Solitary wave dynamics in an external potential Commun. Math. Phys. 250 613-42
24. Jonsson B L G, Fröhlich J, Gustafson S and Sigal I M 2006 Long time motion of NLS solitary waves in a confining potential Ann. Inst. H Poincaré 7 621-60
25. Dejak S I and Sigal I M 2006 Long-time dynamics of KdV solitary waves over a variable bottom Commun. Pure Appl. Math. 59 869-905
26. Dejak S I and Jonsson B L G 2006 Long-time dynamics of variable coefficient mKdV solitary waves J. Math. Phys. 47 1-16
27. Chang S-M, Gustafson S, Nakanishi K and Tsai T-P 2006 Spectra of linearized operators for NLS solitary waves Preprint math.AP/0611483
28. Fröhlich J, Jonsson B L G and Lenzmann E 2007 The kernel condition for boson stars in preparation
29. Demanet L and Schlag W 2006 Numerical verification of a gap condition for linearized NLS Nonlinearity 19 829-52
30. Dieudonné J 1969 Foundations of Modern Analysis (Pure and Applied Mathematics) vol 10-I 3rd edn (New York: Academic) enlarged and corrected printing
31. Lieb E H and Loss M 2001 Analysis (Graduate Studies in Mathematics) vol 14 2nd edn (Providence, RI: American Mathematical Society)
32. Slaggie E L and Wichmann E H 1962 Asymptotic properties of the wave function for a bound nonrelativistic three-body system J. Math. Phys. 3 946-68
33. Hislop P D 2000 Exponential decay of two-body eigenfunctions: a review Proc. Symp. on Mathematical Physics and Quantum Field Theory (Berkeley, CA, 1999) (Electron. J. Differ. Equ. Conf.) vol 4 (San Marcos, TX: Southwest Texas State University) pp 265-88 electronic
34. Stein E M 1993 Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals (Princeton Mathematical Series vol 43) (Princeton, NJ: Princeton University Press) (With the assistance of Timothy S Murphy, Monographs in Harmonic Analysis, III)
35. Kato T 1995 Perturbation Theory for Linear Operators (Classics in Mathematics) (Berlin: Springer) Reprint of the 1980 edition