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Existence and diffusive limit of a two-species kinetic model of chemotaxis
Galactic dynamics in MOND---Existence of equilibria with finite mass and compact support
1. | Fakultät für Mathematik, Physik und Informatik, Universität Bayreuth, D-95440 Bayreuth, Germany |
References:
[1] |
J. Batt, W. Faltenbacher and E. Horst, Stationary spherically symmetric models in stellar dynamics, Arch. Rational Mech. Anal., 93 (1986), 159-183.
doi: 10.1007/BF00279958. |
[2] |
J. Binney and S. Tremaine, Galactic Dynamics, Princeton University Press, Princeton, 1987.
doi: 10.1063/1.2811635. |
[3] |
B. Famaey and S. McGaugh, Modified Newtonian dynamics (MOND): Observational phenomenology and relativistic extensions, Living Rev. Relativity, 15 (2012), p10.
doi: 10.12942/lrr-2012-10. |
[4] |
Y. Guo and G. Rein, Stable steady states in stellar dynamics, Arch. Rational Mech. Anal., 147 (1999), 225-243.
doi: 10.1007/s002050050150. |
[5] |
Y. Guo and G. Rein, A non-variational approach to nonlinear stability in stellar dynamics applied to the King model, Commun. Math. Phys., 271 (2007), 489-509.
doi: 10.1007/s00220-007-0212-8. |
[6] |
M. Lemou, F. Méhats and P. Raphaël, Orbital stability of spherical galactic models, Invent. math., 187 (2012), 145-194.
doi: 10.1007/s00222-011-0332-9. |
[7] |
M. Milgrom, Light and dark in the universe, preprint, arXiv:1203.0954v1. |
[8] |
M. Milgrom, The MOND paradigm, preprint, arXiv:0801.3133. |
[9] |
M. Milgrom, Quasi-linear formulation of MOND, Mon. Not. R. Astron. Soc., 403 (2010), 886-895.
doi: 10.1111/j.1365-2966.2009.16184.x. |
[10] |
M. Núñez, On the gravitational potential of modified Newtonian dynamics, J. Math. Phys., 54 (2013), 082502, 8pp.
doi: 10.1063/1.4817858. |
[11] |
T. Ramming and G. Rein, Spherically symmetric equilibria for self-gravitating kinetic or fluid models in the non-relativistic and relativistic case-A simple proof for finite extension, SIAM J. Math. Anal., 45 (2013), 900-914.
doi: 10.1137/120896712. |
[12] |
G. Rein, Collisionless kinetic equations from astrophysics-The Vlasov-Poisson system, in Handbook of Differential Equations, Evolutionary Equations, Vol. 3 (eds. C. M. Dafermos and E. Feireisl), Elsevier, 2007, 383-476.
doi: 10.1016/S1874-5717(07)80008-9. |
[13] |
G. Rein and A. Rendall, Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics, Math. Proc. Camb.\Phil. Soc., 128 (2000), 363-380.
doi: 10.1017/S0305004199004193. |
[14] |
J. Schaeffer, A class of counterexamples to Jeans' Theorem for the Vlasov-Einstein system, Commun. Math. Phys., 204 (1999), 313-327.
doi: 10.1007/s002200050647. |
show all references
References:
[1] |
J. Batt, W. Faltenbacher and E. Horst, Stationary spherically symmetric models in stellar dynamics, Arch. Rational Mech. Anal., 93 (1986), 159-183.
doi: 10.1007/BF00279958. |
[2] |
J. Binney and S. Tremaine, Galactic Dynamics, Princeton University Press, Princeton, 1987.
doi: 10.1063/1.2811635. |
[3] |
B. Famaey and S. McGaugh, Modified Newtonian dynamics (MOND): Observational phenomenology and relativistic extensions, Living Rev. Relativity, 15 (2012), p10.
doi: 10.12942/lrr-2012-10. |
[4] |
Y. Guo and G. Rein, Stable steady states in stellar dynamics, Arch. Rational Mech. Anal., 147 (1999), 225-243.
doi: 10.1007/s002050050150. |
[5] |
Y. Guo and G. Rein, A non-variational approach to nonlinear stability in stellar dynamics applied to the King model, Commun. Math. Phys., 271 (2007), 489-509.
doi: 10.1007/s00220-007-0212-8. |
[6] |
M. Lemou, F. Méhats and P. Raphaël, Orbital stability of spherical galactic models, Invent. math., 187 (2012), 145-194.
doi: 10.1007/s00222-011-0332-9. |
[7] |
M. Milgrom, Light and dark in the universe, preprint, arXiv:1203.0954v1. |
[8] |
M. Milgrom, The MOND paradigm, preprint, arXiv:0801.3133. |
[9] |
M. Milgrom, Quasi-linear formulation of MOND, Mon. Not. R. Astron. Soc., 403 (2010), 886-895.
doi: 10.1111/j.1365-2966.2009.16184.x. |
[10] |
M. Núñez, On the gravitational potential of modified Newtonian dynamics, J. Math. Phys., 54 (2013), 082502, 8pp.
doi: 10.1063/1.4817858. |
[11] |
T. Ramming and G. Rein, Spherically symmetric equilibria for self-gravitating kinetic or fluid models in the non-relativistic and relativistic case-A simple proof for finite extension, SIAM J. Math. Anal., 45 (2013), 900-914.
doi: 10.1137/120896712. |
[12] |
G. Rein, Collisionless kinetic equations from astrophysics-The Vlasov-Poisson system, in Handbook of Differential Equations, Evolutionary Equations, Vol. 3 (eds. C. M. Dafermos and E. Feireisl), Elsevier, 2007, 383-476.
doi: 10.1016/S1874-5717(07)80008-9. |
[13] |
G. Rein and A. Rendall, Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics, Math. Proc. Camb.\Phil. Soc., 128 (2000), 363-380.
doi: 10.1017/S0305004199004193. |
[14] |
J. Schaeffer, A class of counterexamples to Jeans' Theorem for the Vlasov-Einstein system, Commun. Math. Phys., 204 (1999), 313-327.
doi: 10.1007/s002200050647. |
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