Stationary and static stellar dynamic models with axial symmetry

Nonlinear Analysis, Theory, Methods and Applications

Volumn 41, Issue 3, 2000, Pages 313-344

  Rein, Gerhard ^a,b  

^a INDIANA UNIVERSITY   (United States)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

GALAXIES; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PHASE SPACE METHODS; POISSON DISTRIBUTION; PROBABILITY DENSITY FUNCTION; TRACKING (POSITION); VELOCITY;

AXIAL SYMMETRY; GRAVITATIONAL CONSTANT; SPATIAL MASS DENSITY; STELLAR DYNAMIC MODELS; VLASOV-POISSON SYSTEM;

NONLINEAR SYSTEMS;

EID: 0034230423     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00280-6     Document Type: Article

References (22)

1. C. Bardos, P. Degond, Global existence for the Vlasov Poisson equation in 3 space variables with small initial data, Ann. Inst. Henri Poincaré, Analyse non linéaire 2 (1985) 101-118.
2. J. Batt, H. Berestycki, P. Degond, B. Perthame, Some families of solutions of the Vlasov-Poisson system, Arch. Rational Mech. Anal. 104 (1988) 79-103.
3. J. Batt, W. Faltenbacher, E. Horst, Stationary spherically symmetric models in stellar dynamics, Arch. Rational Mech. Anal. 93 (1986) 159-183.
4. J. Batt, P. Morrison, G. Rein, Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions, Arch. Rational Mech. Anal. 130 (1995) 163-182.
5. K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
6. B. Gidas, W.-M. Ni, L. Nirenberg, Symmetry and related properties via the maximum principle, Commun. Math. Phys. 68 (1979) 209-243.
7. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1983.
8. Y. Guo, W. Strauss, Nonlinear instability of double-humped equilibria, Ann. Inst. Henri Poincaré 12 (1995) 339-352.
9. U. Heilig, On Lichtenstein's analysis of rotating newtonian stars, Ann. Inst. Henri Poincaré, Physique théorique 60 (1994) 457-487.
10. E. Horst, On the asymptotic growth of the solutions of the Vlasov-Poisson system, Math. Methods Appl. Sci. 16 (1993) 75-85.
11. J.D. Jackson, Classical Electrodynamics, Wiley, New York, 1962.
12. L. Lichtenstein, Untersuchung über die Gleichgewichtsfiguren rotierender Flüssigkeiten, deren Teilchen einander nach dem Newtonschen Gesetze anziehen. Erste Abhandlung. Homogene Flüssigkeiten. Allgemeine Existenzsätze, Math. Z. 1 (1918) 229-284.
13. L. Lichtenstein, Gleichgewichtsfiguren Rotierender Flüssigkeiten, Springer, Berlin, 1933.
14. P.-L. Lions, B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math. 105 (1991) 415-430.
15. K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Eqns. 95 (1992) 281-303.
16. G. Rein, Existence of stationary, collisionless plasmas on bounded domains, Math. Methods Appl. Sci. 15 (1992) 365-374.
17. G. Rein, Nonlinear stability for the Vlasov-Poisson system - the energy-Casimir method, Math. Methods Appl. Sci. 17 (1994) 1129-1140.
18. G. Rein, Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system, Banach Center Publications, Warsaw, Vol. 41 part I, 1997, pp. 179-194.
19. G. Rein, Nonlinear stability of homogeneous models in Newtonian cosmology, Arch. Rational Mech. Anal. 140 (1997) 335-351.
20. G. Rein, A.D. Rendall, Global existence of classical solutions to the Vlasov-Poisson system in a three-dimensional, cosmological setting, Arch. Rational Mech. Anal. 126 (1994) 183-201.
21. J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Commun. Part. Differential Equations 16 (1991) 1313-1335.
22. G. Wolansky, On nonlinear stability of polytropic galaxies, Preprint 1995.