-
Previous Article
A remark on the ultra-analytic smoothing properties of the spatially homogeneous Landau equation
- KRM Home
- This Issue
-
Next Article
Cauchy problem on the Vlasov-Fokker-Planck equation coupled with the compressible Euler equations through the friction force
Unstable galaxy models
1. | School of Mathematical Sciences, Peking University, Beijing, 100871, China, China |
2. | Division of Applied Mathematics, Brown University, Providence, RI 02912, United States |
3. | School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States |
References:
[1] |
V. A. Antonov, Remarks on the problem of stability in stellar dynamics,, Soviet Astr. J., 4 (1960), 859.
|
[2] |
V. A. Antonov, Solution of the Problem of Stability of Stellar System Emden'S Density Law and the Spherical Distribution of Velocities,, Vestnik Leningradskogo Universiteta, (1962). Google Scholar |
[3] |
J. Barnes, P. Hut and J. Goodman, Dynamical instabilities in spherical stellar systems,, Astrophysical Journal, 300 (1986), 112.
doi: 10.1086/163786. |
[4] |
P. Bartholomew, On the theory of stability of galaxies,, Monthly Notices of the Royal Astronomical Society, 151 (1971), 333. Google Scholar |
[5] |
G. Bertin, Dynamics of Galaxies,, Cambridge University Press, (2000).
|
[6] |
J. Binney and S. Tremaine, Galactic Dynamics (2nd Edition),, Princeton University Press, (2008). Google Scholar |
[7] |
J. P. Doremus, M. R. Feix and G. Baumann, Stability of encounterless spherical stellar systems,, Phys. Rev. Letts, 26 (1971), 725. Google Scholar |
[8] |
D. Gillon, M. Cantus, J. P. Doremus and G. Baumann, Stability of self-gravitating spherical systems in which phase space density is a function of energy and angular momentum, for spherical perturbations,, Astronomy and Astrophysics, 50 (1976), 467.
|
[9] |
A. Fridman and V. Polyachenko, Physics of Gravitating System Vol I,, Springer-Verlag, (1984). Google Scholar |
[10] |
J. Goodman, An instability test for nonrotating galaxies,, Astrophysical Journal, 329 (1988), 612.
doi: 10.1086/166407. |
[11] |
Y. Guo and Z. Lin, Unstable and stable galaxy models,, Commun. Math. Phys., 279 (2008), 789.
doi: 10.1007/s00220-008-0439-z. |
[12] |
M. Henon, Numerical experiments on the stability of spherical stellar systems,, Astronomy and Astrophysics, 24 (1973), 229. Google Scholar |
[13] |
Y. Guo and G. Rein, A non-variational approach to nonlinear stability in stellar dynamics applied to the King model,, Comm. Math. Phys., 271 (2007), 489.
doi: 10.1007/s00220-007-0212-8. |
[14] |
H. Kandrup and J. F. Signet, A simple proof of dynamical stability for a class of spherical clusters,, The Astrophys. J., 298 (1985), 27.
doi: 10.1086/163586. |
[15] |
H. Kandrup, A stability criterion for any collisionless stellar equilibrium and some concrete applications thereof,, Astrophysical Journal, 370 (1991), 312. Google Scholar |
[16] |
D. Merritt, Elliptical galaxy dynamics,, The Publications of the Astronomical Society of the Pacific, 111 (1999), 129. Google Scholar |
[17] |
P. L. Palmer, Stability of Collisionless Stellar Systems: Mechanisms for the Dynamical Structure of Galaxies,, Kluwer Academic Publishers, (1994). Google Scholar |
[18] |
J. Perez and J. Aly, Stability of spherical stellar systems - I. Analytical results,, Monthly Notices of the Royal Astronomical Society, 280 (1996), 689.
doi: 10.1093/mnras/280.3.689. |
[19] |
J. F. Sygnet, G. des Forets, M. Lachieze-Rey and R. Pellat, Stability of gravitational systems and gravothermal catastrophe in astrophysics,, Astrophysical Journal, 276 (1984), 737. Google Scholar |
[20] |
G. Rein and A. D. Rendall, Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics,, Math. Proc. Camb Phil. Soc., 128 (2000), 363.
doi: 10.1017/S0305004199004193. |
show all references
References:
[1] |
V. A. Antonov, Remarks on the problem of stability in stellar dynamics,, Soviet Astr. J., 4 (1960), 859.
|
[2] |
V. A. Antonov, Solution of the Problem of Stability of Stellar System Emden'S Density Law and the Spherical Distribution of Velocities,, Vestnik Leningradskogo Universiteta, (1962). Google Scholar |
[3] |
J. Barnes, P. Hut and J. Goodman, Dynamical instabilities in spherical stellar systems,, Astrophysical Journal, 300 (1986), 112.
doi: 10.1086/163786. |
[4] |
P. Bartholomew, On the theory of stability of galaxies,, Monthly Notices of the Royal Astronomical Society, 151 (1971), 333. Google Scholar |
[5] |
G. Bertin, Dynamics of Galaxies,, Cambridge University Press, (2000).
|
[6] |
J. Binney and S. Tremaine, Galactic Dynamics (2nd Edition),, Princeton University Press, (2008). Google Scholar |
[7] |
J. P. Doremus, M. R. Feix and G. Baumann, Stability of encounterless spherical stellar systems,, Phys. Rev. Letts, 26 (1971), 725. Google Scholar |
[8] |
D. Gillon, M. Cantus, J. P. Doremus and G. Baumann, Stability of self-gravitating spherical systems in which phase space density is a function of energy and angular momentum, for spherical perturbations,, Astronomy and Astrophysics, 50 (1976), 467.
|
[9] |
A. Fridman and V. Polyachenko, Physics of Gravitating System Vol I,, Springer-Verlag, (1984). Google Scholar |
[10] |
J. Goodman, An instability test for nonrotating galaxies,, Astrophysical Journal, 329 (1988), 612.
doi: 10.1086/166407. |
[11] |
Y. Guo and Z. Lin, Unstable and stable galaxy models,, Commun. Math. Phys., 279 (2008), 789.
doi: 10.1007/s00220-008-0439-z. |
[12] |
M. Henon, Numerical experiments on the stability of spherical stellar systems,, Astronomy and Astrophysics, 24 (1973), 229. Google Scholar |
[13] |
Y. Guo and G. Rein, A non-variational approach to nonlinear stability in stellar dynamics applied to the King model,, Comm. Math. Phys., 271 (2007), 489.
doi: 10.1007/s00220-007-0212-8. |
[14] |
H. Kandrup and J. F. Signet, A simple proof of dynamical stability for a class of spherical clusters,, The Astrophys. J., 298 (1985), 27.
doi: 10.1086/163586. |
[15] |
H. Kandrup, A stability criterion for any collisionless stellar equilibrium and some concrete applications thereof,, Astrophysical Journal, 370 (1991), 312. Google Scholar |
[16] |
D. Merritt, Elliptical galaxy dynamics,, The Publications of the Astronomical Society of the Pacific, 111 (1999), 129. Google Scholar |
[17] |
P. L. Palmer, Stability of Collisionless Stellar Systems: Mechanisms for the Dynamical Structure of Galaxies,, Kluwer Academic Publishers, (1994). Google Scholar |
[18] |
J. Perez and J. Aly, Stability of spherical stellar systems - I. Analytical results,, Monthly Notices of the Royal Astronomical Society, 280 (1996), 689.
doi: 10.1093/mnras/280.3.689. |
[19] |
J. F. Sygnet, G. des Forets, M. Lachieze-Rey and R. Pellat, Stability of gravitational systems and gravothermal catastrophe in astrophysics,, Astrophysical Journal, 276 (1984), 737. Google Scholar |
[20] |
G. Rein and A. D. Rendall, Compact support of spherically symmetric equilibria in non-relativistic and relativistic galactic dynamics,, Math. Proc. Camb Phil. Soc., 128 (2000), 363.
doi: 10.1017/S0305004199004193. |
[1] |
Katherine Zhiyuan Zhang. Focusing solutions of the Vlasov-Poisson system. Kinetic & Related Models, 2019, 12 (6) : 1313-1327. doi: 10.3934/krm.2019051 |
[2] |
Blanca Ayuso, José A. Carrillo, Chi-Wang Shu. Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system. Kinetic & Related Models, 2011, 4 (4) : 955-989. doi: 10.3934/krm.2011.4.955 |
[3] |
Silvia Caprino, Guido Cavallaro, Carlo Marchioro. Time evolution of a Vlasov-Poisson plasma with magnetic confinement. Kinetic & Related Models, 2012, 5 (4) : 729-742. doi: 10.3934/krm.2012.5.729 |
[4] |
Gang Li, Xianwen Zhang. A Vlasov-Poisson plasma of infinite mass with a point charge. Kinetic & Related Models, 2018, 11 (2) : 303-336. doi: 10.3934/krm.2018015 |
[5] |
Jack Schaeffer. Global existence for the Vlasov-Poisson system with steady spatial asymptotic behavior. Kinetic & Related Models, 2012, 5 (1) : 129-153. doi: 10.3934/krm.2012.5.129 |
[6] |
Gianluca Crippa, Silvia Ligabue, Chiara Saffirio. Lagrangian solutions to the Vlasov-Poisson system with a point charge. Kinetic & Related Models, 2018, 11 (6) : 1277-1299. doi: 10.3934/krm.2018050 |
[7] |
Zili Chen, Xiuting Li, Xianwen Zhang. The two dimensional Vlasov-Poisson system with steady spatial asymptotics. Kinetic & Related Models, 2017, 10 (4) : 977-1009. doi: 10.3934/krm.2017039 |
[8] |
Meixia Xiao, Xianwen Zhang. On global solutions to the Vlasov-Poisson system with radiation damping. Kinetic & Related Models, 2018, 11 (5) : 1183-1209. doi: 10.3934/krm.2018046 |
[9] |
Jean Dolbeault. An introduction to kinetic equations: the Vlasov-Poisson system and the Boltzmann equation. Discrete & Continuous Dynamical Systems - A, 2002, 8 (2) : 361-380. doi: 10.3934/dcds.2002.8.361 |
[10] |
Silvia Caprino, Guido Cavallaro, Carlo Marchioro. A Vlasov-Poisson plasma with unbounded mass and velocities confined in a cylinder by a magnetic mirror. Kinetic & Related Models, 2016, 9 (4) : 657-686. doi: 10.3934/krm.2016011 |
[11] |
Hyung Ju Hwang, Jaewoo Jung, Juan J. L. Velázquez. On global existence of classical solutions for the Vlasov-Poisson system in convex bounded domains. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 723-737. doi: 10.3934/dcds.2013.33.723 |
[12] |
Francis Filbet, Roland Duclous, Bruno Dubroca. Analysis of a high order finite volume scheme for the 1D Vlasov-Poisson system. Discrete & Continuous Dynamical Systems - S, 2012, 5 (2) : 283-305. doi: 10.3934/dcdss.2012.5.283 |
[13] |
Dongming Wei. 1D Vlasov-Poisson equations with electron sheet initial data. Kinetic & Related Models, 2010, 3 (4) : 729-754. doi: 10.3934/krm.2010.3.729 |
[14] |
Joackim Bernier, Michel Mehrenberger. Long-time behavior of second order linearized Vlasov-Poisson equations near a homogeneous equilibrium. Kinetic & Related Models, 2020, 13 (1) : 129-168. doi: 10.3934/krm.2020005 |
[15] |
Pablo Cincotta, Claudia Giordano, Juan C. Muzzio. Global dynamics in a self--consistent model of elliptical galaxy. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 439-454. doi: 10.3934/dcdsb.2008.10.439 |
[16] |
Sebastián Ferrer, Francisco Crespo. Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Journal of Geometric Mechanics, 2014, 6 (4) : 479-502. doi: 10.3934/jgm.2014.6.479 |
[17] |
Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic & Related Models, 2009, 2 (4) : 707-725. doi: 10.3934/krm.2009.2.707 |
[18] |
Faker Ben Belgacem. Uniqueness for an ill-posed reaction-dispersion model. Application to organic pollution in stream-waters. Inverse Problems & Imaging, 2012, 6 (2) : 163-181. doi: 10.3934/ipi.2012.6.163 |
[19] |
Robert T. Glassey, Walter A. Strauss. Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system. Discrete & Continuous Dynamical Systems - A, 1999, 5 (3) : 457-472. doi: 10.3934/dcds.1999.5.457 |
[20] |
Hyung Ju Hwang, Juhi Jang. On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian. Discrete & Continuous Dynamical Systems - B, 2013, 18 (3) : 681-691. doi: 10.3934/dcdsb.2013.18.681 |
2018 Impact Factor: 1.38
Tools
Metrics
Other articles
by authors
[Back to Top]