Team > Prof. Dr. Gerhard Rein

2023

Rein, Gerhard
Stability and instability results for equilibria of a (relativistic) self-gravitating collision ...
In: Classical and Quantum Gravity Bd. 40 (2023)
doi:10.1088/1361-6382/acf436 ...

2022

Günther, Sebastian; Rein, Gerhard
The Einstein-Vlasov system in maximal areal coordinates : Local existence and continuation
In: Kinetic & Related Models Bd. 15 (2022) Heft 4. - S. 681-719
doi:10.3934/krm.2021040 ...

Hadžić, Mahir; Rein, Gerhard; Straub, Christopher
On the Existence of Linearly Oscillating Galaxies
In: Archive for Rational Mechanics and Analysis Bd. 243 (2022) . - S. 611-696
doi:10.1007/s00205-021-01734-4 ...

2021

Günther, Sebastian; Straub, Christopher; Rein, Gerhard
Collisionless Equilibria in General Relativity : Stable Configurations beyond the First Binding ...
In: The Astrophysical Journal Bd. 918 (2021) Heft 2
doi:10.3847/1538-4357/ac0eef ...

Günther, Sebastian; Körner, Jacob; Lebeda, Timo; Pötzl, Bastian; Rein, Gerhard; Straub, Christopher; Weber, Jörg
A numerical stability analysis for the Einstein–Vlasov system
In: Classical and Quantum Gravity Bd. 38 (2021) Heft 3
doi:10.1088/1361-6382/abcbdf ...

Hadžić, Mahir; Lin, Zhiwu; Rein, Gerhard
Stability and instability of self-gravitating relativistic matter distributions
In: Archive for Rational Mechanics and Analysis Bd. 241 (2021) . - S. 1-89
doi:10.1007/s00205-021-01647-2 ...

Körner, Jacob; Rein, Gerhard
Strong Lagrangian solutions of the (relativistic) Vlasov-Poisson system for non-smooth, spheric ...
In: SIAM Journal on Mathematical Analysis Bd. 53 (2021) Heft 4. - S. 4985-4996
doi:10.1137/20M1378910 ...

2020

Rein, Gerhard; Straub, Christopher
On the transport operators arising from linearizing the Vlasov-Poisson or Einstein-Vlasov syste ...
In: Kinetic & Related Models Bd. 13 (2020) Heft 5. - S. 933-949
doi:10.3934/krm.2020032 ...

2018

Rein, Gerhard
The asymptotic behavior of solutions to the repulsive n-body problem
In: SIAM Journal on Mathematical Analysis Bd. 50 (2018) Heft 1. - S. 1-4
doi:10.1137/17M1116271 ...

Ramming, Tobias; Rein, Gerhard
Oscillating solutions of the Vlasov–Poisson system : A numerical investigation
In: Physica D: Nonlinear Phenomena Bd. 365 (2018) . - S. 72-79
doi:10.1016/j.physd.2017.10.013 ...

2017

Ramming, Tobias; Rein, Gerhard
Mass-radius spirals for steady state families of the Vlasov-Poisson system
In: Archive for Rational Mechanics and Analysis Bd. 224 (2017) . - S. 1127-1159
doi:10.1007/s00205-017-1098-z ...

2016

Rein, Gerhard; Taegert, Lukas
Gravitational collapse and the Vlasov-Poisson system
In: Annales Henri Poincaré Bd. 17 (2016) Heft 6. - S. 1415-1427
doi:10.1007/s00023-015-0424-y ...

2015

Rein, Gerhard
Galactic dynamics in MOND : Existence of equilibria with finite mass and compact support
In: Kinetic & Related Models Bd. 8 (2015) Heft 2. - S. 381-394
doi:10.3934/krm.2015.8.381 ...

Andréasson, Håkan; Rein, Gerhard
On the rotation curves for axially symmetric disk solutions of the Vlasov-Poisson system
In: Monthly Notices of the Royal Astronomical Society Bd. 446 (2015) Heft 4. - S. 3932-3942
doi:10.1093/mnras/stu2346 ...

Hadžić, Mahir; Rein, Gerhard
On the small redshift limit of steady states of the spherically symmetric Einstein-Vlasov syste ...
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 159 (2015) Heft 3. - S. 529-546
doi:10.1017/S0305004115000511 ...

2014

Andréasson, Håkan; Kunze, Markus; Rein, Gerhard
Rotating, stationary, axially symmetric spacetimes with collisionless matter
In: Communications in Mathematical Physics Bd. 329 (2014) Heft 2. - S. 787-808
doi:10.1007/s00220-014-1904-5 ...

2013

Korch, Matthias; Ramming, Tobias; Rein, Gerhard
Parallelization of particle-in-cell codes for nonlinear kinetic models from mathematical physic ...
International Conference on Parallel Processing, The 42nd Annual Conference ICPP 2013 : Proceedings ; 1 - 4 October 2013 Lyon, France
Los Alamitos, CA : IEEE, 2013. - S. 523-529
doi:10.1109/ICPP.2013.65 ...

Ramming, Tobias; Rein, Gerhard
Spherically symmetric equilibria for self-gravitating kinetic or fluid models in the non-relati ...
In: SIAM Journal on Mathematical Analysis Bd. 45 (2013) Heft 2. - S. 900-914
doi:10.1137/120896712 ...

Hadžić, Mahir; Rein, Gerhard
Stability for the spherically symmetric Einstein-Vlasov system : a coercivity estimate
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 155 (2013) Heft 3. - S. 529-556
doi:10.1017/S030500411300056X ...

2011

Andréasson, Håkan; Kunze, Markus; Rein, Gerhard
Existence of axially symmetric static solutions of the Einstein-Vlasov system
In: Communications in Mathematical Physics Bd. 308 (2011) . - S. 23-47
doi:10.1007/s00220-011-1324-8 ...

Andréasson, Håkan; Kunze, Markus; Rein, Gerhard
The formation of black holes in spherically symmetric gravitational collapse
In: Mathematische Annalen Bd. 350 (2011) Heft 3. - S. 683-705
doi:10.1007/s00208-010-0578-3 ...

2010

Andréasson, Håkan; Rein, Gerhard
The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravit ...
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 149 (2010) Heft 1. - S. 173-188
doi:10.1017/S0305004109990454 ...

Andréasson, Håkan; Rein, Gerhard
Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system
In: Journal of Hyperbolic Differential Equations Bd. 7 (2010) Heft 4. - S. 707-731
doi:10.1142/S0219891610002268 ...

Andréasson, Håkan; Kunze, Markus; Rein, Gerhard
Gravitational collapse and the formation of black holes for the spherically symmetric Einstein- ...
In: Quarterly of Applied Mathematics Bd. 68 (2010) Heft 1. - S. 17-42
http://www.ams.org/journals/qam/2010-68-01/S0033-5 ...

2009

Firt, Roman; Rein, Gerhard; Seehafer, Martin
Flat galaxies with dark matter halos : existence and stability
In: Communications in Mathematical Physics Bd. 291 (2009) Heft 1. - S. 225-255
doi:10.1007/s00220-009-0872-7 ...

Andréasson, Håkan; Rein, Gerhard; Eklund, Mikael
A numerical investigation of the steady states of the spherically symmetric Einstein-Vlasov-Max ...
In: Classical and Quantum Gravity Bd. 26 (2009) Heft 14
doi:10.1088/0264-9381/26/14/145003 ...

2008

Andréasson, Håkan; Kunze, Markus; Rein, Gerhard
Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter
In: Communications in Partial Differential Equations Bd. 33 (2008) Heft 4. - S. 656-668
doi:10.1080/03605300701454883 ...

2007

Rein, Gerhard
Collisionless Kinetic Equations from Astrophysics : The Vlasov-Poisson System
Dafermos,Constantine M.; Feireisl, E. (Hrsg.): Handbook of Differential Equations : Evolutionary Equations. Vol. 3
Amsterdam : Elsevier, 2007. - S. 383-476
doi:10.1016/S1874-5717(07)80008-9 ...

Hadžić, Mahir; Rein, Gerhard
Global existence and nonlinear stability for the relativistic Vlasov-Poisson system in the grav ...
In: Indiana University Mathematics Journal Bd. 56 (2007) Heft 5. - S. 2453-2488
doi:10.1512/iumj.2007.56.3064 ...

Guo, Yan; Rein, Gerhard
A non-variational approach to nonlinear stability in stellar dynamics applied to the King model
In: Communications in Mathematical Physics Bd. 271 (2007) Heft 2. - S. 489-509
doi:10.1007/s00220-007-0212-8 ...

Andréasson, Håkan; Rein, Gerhard
On the steady states of the spherically symmetric Einstein-Vlasov system
In: Classical and Quantum Gravity Bd. 24 (2007) Heft 7. - S. 1809-1832
doi:10.1088/0264-9381/24/7/008 ...

2006

Bauer, Sebastian; Kunze, Markus; Rein, Gerhard; Rendall, Alan D.
Multipole radiation in a collisionless gas coupled to electromagnetism or scalar gravitation
In: Communications in Mathematical Physics Bd. 266 (2006) Heft 1. - S. 267-288
doi:10.1007/s00220-006-0015-3 ...

Andréasson, Håkan; Rein, Gerhard
A numerical investigation of the stability of steady states and critical phenomena for the sphe ...
In: Classical and Quantum Gravity Bd. 23 (2006) Heft 11. - S. 3659-3677
doi:10.1088/0264-9381/23/11/001 ...

Firt, Roman; Rein, Gerhard
Stability of disk-like galaxies : Part I: Stability via reduction
In: Analysis Bd. 26 (2006) Heft 4. - S. 507-525
doi:10.1524/anly.2006.26.4.507 ...

2005

Andréasson, Håkan; Calogero, Simone; Rein, Gerhard
Global classical solutions to the spherically symmetric Nordström-Vlasov system
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 138 (2005) Heft 3. - S. 533-539
doi:10.1017/S0305004105008467 ...

Rein, Gerhard
Nonlinear Stability of Newtonian Galaxies and Stars from a Mathematical Perspective
In: Annals of the New York Academy of Sciences Bd. 1045 (2005) . - S. 103-119
doi:10.1196/annals.1350.010 ...

Kunzinger, Michael; Rein, Gerhard; Steinbauer, Roland; Teschl, Gerald
On classical solutions of the relativistic Vlasov-Klein-Gordon system
In: Electronic Journal of Differential Equations Bd. 2005 (2005) Heft 1. - S. 1-17
http://www.emis.de/journals/EJDE/Volumes/2005/01/k ...

2004

Calogero, Simone; Rein, Gerhard
Global weak solutions to the Nordström-Vlasov system
In: Journal of Differential Equations Bd. 204 (2004) Heft 2. - S. 323-338
doi:10.1016/j.jde.2004.02.011 ...

Rein, Gerhard
Global weak solutions to the relativistic Vlasov-Maxwell system revisited
In: Communications in Mathematical Sciences Bd. 2 (2004) Heft 2. - S. 145-158
doi:10.4310/CMS.2004.v2.n2.a1 ...

Rein, Gerhard
On future geodesic completeness for the Einstein-Vlasov system with hyperbolic symmetry
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 137 (2004) Heft 1. - S. 237-244
doi:10.1017/S0305004103007485 ...

2003

Rein, Gerhard; Rodewis, Thomas
Convergence of a particle-in-cell scheme for the spherically symmetric Vlasov-Einstein system
In: Indiana University Mathematics Journal Bd. 52 (2003) Heft 4. - S. 821-862
doi:10.1512/iumj.2003.52.2363 ...

Kunzinger, Michael; Rein, Gerhard; Steinbauer, Roland; Teschl, Gerald
Global weak solutions of the relativistic Vlasov-Klein-Gordon system
In: Communications in Mathematical Physics Bd. 238 (2003) Heft 1-2. - S. 367-378
doi:10.1007/s00220-003-0861-1 ...

Rein, Gerhard
Non-linear stability of gaseous stars
In: Archive for Rational Mechanics and Analysis Bd. 168 (2003) Heft 2. - S. 115-130
doi:10.1007/s00205-003-0260-y ...

Calogero, Simone; Rein, Gerhard
On classical solutions of the Nordström-Vlasov system
In: Communications in Partial Differential Equations Bd. 28 (2003) Heft 11-12. - S. 1863-1885
doi:10.1081/PDE-120025488 ...

Andréasson, Håkan; Rein, Gerhard; Rendall, Alan D.
On the Einstein-Vlasov system with hyperbolic symmetry
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 134 (2003) Heft 3. - S. 529-549
doi:10.1017/S0305004102006606 ...

Guo, Yan; Rein, Gerhard
Stable models of elliptical galaxies
In: Monthly Notices of the Royal Astronomical Society Bd. 344 (2003) Heft 4. - S. 1296-1306
doi:10.1046/j.1365-8711.2003.06920.x ...

2002

Markowich, Peter A.; Rein, Gerhard; Wolansky, Gershon
Existence and nonlinear stability of steady states of the Schrödinger-Poisson system
In: Journal of Statistical Physics Bd. 106 (2002) Heft 5-6. - S. 1221-1239
doi:10.1023/A:1014050206769 ...

Rein, Gerhard
Reduction and a concentration-compactness principle for energy-Casimir functionals
In: SIAM Journal on Mathematical Analysis Bd. 33 (2002) Heft 4. - S. 896-912
doi:10.1137/P0036141001389275 ...

Rein, Gerhard
Stability of spherically symmetric steady states in galactic dynamics against general perturbat ...
In: Archive for Rational Mechanics and Analysis Bd. 161 (2002) Heft 1. - S. 27-42
doi:10.1007/s002050100167 ...

2001

Guo, Yan; Rein, Gerhard
Isotropic steady states in galactic dynamics
In: Communications in Mathematical Physics Bd. 219 (2001) . - S. 607-629
doi:10.1007/s002200100434 ...

Dolbeault, Jean; Rein, Gerhard
Time-dependent rescalings and Lyapunov functionals for the Vlasov-Poisson and Euler-Poisson sys ...
In: Mathematical Models and Methods in Applied Sciences Bd. 11 (2001) Heft 3. - S. 407-432
doi:10.1142/S021820250100091X ...

2000

Rein, Gerhard; Rendall, Alan D.
Compact support of spherically symmetric equilibria in non-relativistic and relativistic galac ...
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 128 (2000) Heft 2. - S. 363-380

Rein, Gerhard
Stationary and static stellar dynamic models with axial symmetry
In: Nonlinear Analysis : Theory, Methods & Applications Bd. 41 (2000) Heft 3-4. - S. 313-344
doi:10.1016/S0362-546X(98)00280-6 ...

1999

Guo, Yan; Rein, Gerhard
Existence and stability of Camm type steady states in galactic dynamics
In: Indiana University Mathematics Journal Bd. 48 (1999) Heft 4. - S. 1237-1255
doi:10.1512/iumj.1999.48.1819 ...

Rein, Gerhard
Flat steady states in stellar dynamics : existence and stability
In: Communications in Mathematical Physics Bd. 205 (1999) Heft 1. - S. 229-247
doi:10.1007/s002200050674 ...

Braasch, Peter; Rein, Gerhard; Vukadinovic, Jesenko
Nonlinear stability of stationary plasmas : an extension of the energy-Casimir method
In: SIAM Journal on Applied Mathematics Bd. 59 (1999) Heft 3. - S. 831-844
doi:10.1137/S0036139997329069 ...

Guo, Yan; Rein, Gerhard
Stable steady states in stellar dynamics
In: Archive for Rational Mechanics and Analysis Bd. 147 (1999) Heft 3. - S. 225-243
doi:10.1007/s002050050150 ...

Rein, Gerhard
Static shells for the Vlasov-Poisson and Vlasov-Einstein systems
In: Indiana University Mathematics Journal Bd. 48 (1999) Heft 1. - S. 335-346
doi:10.1512/iumj.1999.48.1636 ...

1998

Rein, Gerhard; Rendall, Alan D.; Schaeffer, Jack
Critical collapse of collisionless matter : A numerical investigation
In: Physical Review D Bd. 58 (1998) Heft 4
doi:10.1103/PhysRevD.58.044007 ...

Rein, Gerhard
Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case
In: Mathematische Nachrichten Bd. 191 (1998) Heft 1. - S. 269-278
doi:10.1002/mana.19981910114 ...

Batt, Jürgen; Kunze, Markus; Rein, Gerhard
On the asymptotic behaviour of a one-dimensional monocharged plasma and a rescaling method
In: Advances in Differential Equations Bd. 3 (1998) Heft 2. - S. 271-292

1997

Rein, Gerhard
Nonlinear stability of homogeneous models in Newtonian cosmology
In: Archive for Rational Mechanics and Analysis Bd. 140 (1997) Heft 4. - S. 335-351
doi:10.1007/s002050050070 ...

Rein, Gerhard
Selfgravitating systems in Newtonian theory : the Vlasov-Poisson system
In: Banach Center Publications Bd. 41 (1997) Heft 1. - S. 179-194
http://matwbn.icm.edu.pl/ksiazki/bcp/bcp41/bcp4111 ...

1996

Rein, Gerhard
Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symm ...
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 119 (1996) Heft 4. - S. 739-762
doi:10.1017/S0305004100074569 ...

Rein, Gerhard; Rendall, Alan D.
Erratum: Global existence of solutions of the spherically symmetric Vlasov-Einstein system with ...
In: Communications in Mathematical Physics Bd. 176 (1996) Heft 2. - S. 475-478
doi:10.1007/BF02099559 ...

Illner, Reinhard; Rein, Gerhard
Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case
In: Mathematical Methods in the Applied Sciences Bd. 19 (1996) Heft 17. - S. 1409-1413
doi:10.1002/(SICI)1099-1476(19961125)19:17<1409::A ...

1995

Batt, Jürgen; Morrison, Philip J.; Rein, Gerhard
Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions
In: Archive for Rational Mechanics and Analysis Bd. 130 (1995) Heft 2. - S. 163-182
doi:10.1007/BF00375154 ...

Rein, Gerhard; Rendall, Alan D.; Schaeffer, Jack
A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system
In: Communications in Mathematical Physics Bd. 168 (1995) Heft 3. - S. 467-478
doi:10.1007/BF02101839 ...

1994

Rein, Gerhard; Rendall, Alan D.
Global existence of classical solutions to the Vlasov-Poisson system in a three-dimensional, co ...
In: Archive for Rational Mechanics and Analysis Bd. 126 (1994) Heft 2. - S. 183-201
doi:10.1007/BF00391558 ...

Rein, Gerhard
Non-linear stability for the Vlasov-Poisson system : the energy-Casimir method
In: Mathematical Methods in the Applied Sciences Bd. 17 (1994) Heft 14. - S. 1129-1140
doi:10.1002/mma.1670171404 ...

Rein, Gerhard
Static solutions of the spherically symmetric Vlasov-Einstein system
In: Mathematical Proceedings of the Cambridge Philosophical Society Bd. 115 (1994) Heft 3. - S. 559-570
doi:10.1017/S0305004100072303 ...

1993

Batt, Jürgen; Rein, Gerhard
A rigorous stability result for the Vlasov-Poisson system in three dimensions
In: Anali di Matematica Pura ed Applicata Bd. 164 (1993) Heft 1. - S. 133-154
doi:10.1007/BF01759319 ...

Rein, Gerhard; Rendall, Alan D.
Smooth static solutions of the spherically symmetric Vlasov-Einstein system
In: Annales de l'Institut Henri Poincaré A Bd. 59 (1993) Heft 4. - S. 383-397
http://archive.numdam.org/ARCHIVE/AIHPA/AIHPA_1993 ...

1992

Rein, Gerhard
Existence of stationary, collisionless plasmas in bounded domains
In: Mathematical Methods in the Applied Sciences Bd. 15 (1992) Heft 5. - S. 365-374
doi:10.1002/mma.1670150507 ...

Rein, Gerhard; Weckler, Jürgen
Generic global classical solutions of the Vlasov-Fokker-Planck-Poisson system in three dimensio ...
In: Journal of Differential Equations Bd. 99 (1992) Heft 1. - S. 59-77
doi:10.1016/0022-0396(92)90135-A ...

Rein, Gerhard; Rendall, Alan D.
Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small in ...
In: Communications in Mathematical Physics Bd. 150 (1992) Heft 3. - S. 561-583
doi:10.1007/BF02096962 ...

Rein, Gerhard; Rendall, Alan D.
The Newtonian limit of the spherically symmetric Vlasov-Einstein system
In: Communications in Mathematical Physics Bd. 150 (1992) Heft 3. - S. 585-591
doi:10.1007/BF02096963 ...

Kruse, Kai-Olaf; Rein, Gerhard
A stability result for the relativistic Vlasov-Maxwell system
In: Archive for Rational Mechanics and Analysis Bd. 121 (1992) Heft 2. - S. 187-203
doi:10.1007/BF00375417 ...

1991

Batt, Jürgen; Rein, Gerhard
Global classical solutions of the periodic Vlasov-Poisson system
In: Comptes Rendus de l'Académie des Sciences. Series I Bd. 313 (1991) . - S. 411-416

1990

Rein, Gerhard
Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics
In: Communications in Mathematical Physics Bd. 135 (1990) Heft 1. - S. 41-78
doi:10.1007/BF02097656 ...

Rein, Gerhard
A two-species plasma in the limit of large ion mass
In: Mathematical Methods in the Applied Sciences Bd. 13 (1990) Heft 2. - S. 159-167
doi:10.1002/mma.1670130206 ...

1987

Farin, Gerald; Rein, Gerhard; Sapidis, Nikolas; Worsey, Andrew
Fairing cubic b-spline curves
In: Computer Aided Geometric Design Bd. 4 (1987) Heft 1-2. - S. 91-103
doi:10.1016/0167-8396(87)90027-6 ...