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Team > Prof. Dr. Gerhard Rein

Overview
Overview
Prof. Dr. Gerhard Rein Prof. Dr. Gerhard Rein
Prof. Dr. Gerhard Rein

Fakultät für Mathematik, Physik und Informatik
Mathematisches Institut


Research Interests

Nonlinear partial differential equations for the description of large ensembles of particles interacting via self-consistent forces, e.g.

  • Vlasov-Poisson system,
  • Vlasov-Maxwell system,
  • Einstein-Vlasov system,

motivated by problems from astrophysics (dynamics of galaxies, formation of black holes) and plasma physics. Typical questions:

  • initial value problem, local/global existence,
  • stationary solutions and their stability or instability,
  • time periodic, pulsating solutions,
  • gravitational collapse.

Profiles


Prof. Dr. Gerhard Rein

Fakultät für Mathematik, Physik und Informatik
Mathematisches Institut


Publications

2021

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

Günther, Sebastian; Straub, Christopher; Rein, Gerhard
Collisionless Equilibria in General Relativity : Stable Configurations beyond the First Binding ...
in The Astrophysical Journal volume 918 (2021) issue 2. - page 48
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 volume 38 (2021) issue 3. - page No. 035003
doi:10.1088/1361-6382/abcbdf ...

Körner, Jacob; Rein, Gerhard
Strong Lagrangian solutions of the (relativistic) Vlasov-Poisson system for non-smooth, spheric ...
in SIAM Journal on Mathematical Analysis volume 53 (2021) issue 4. - page 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 and Related Models volume 13 (2020) issue 5. - page 933-949
doi:10.3934/krm.2020032 ...

2018

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

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

2017

Ramming, Tobias; Rein, Gerhard
Mass-radius spirals for steady state families of the Vlasov-Poisson system
in Archive for Rational Mechanics and Analysis volume 224 (2017) issue 3. - page 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 volume 17 (2016) issue 6. - page 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 and Related Models volume 8 (2015) issue 2. - page 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 volume 446 (2015) issue 4. - page 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 volume 159 (2015) issue 3. - page 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 volume 329 (2014) issue 2. - page 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. - page 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 volume 45 (2013) issue 2. - page 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 volume 155 (2013) issue 3. - page 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 volume 308 (2011) . - page 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 volume 350 (2011) issue 3. - page 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 volume 149 (2010) issue 1. - page 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 volume 7 (2010) issue 4. - page 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 volume 68 (2010) issue 1. - page 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 volume 291 (2009) issue 1. - page 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 volume 26 (2009) issue 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 volume 33 (2008) issue 4. - page 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. - page 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 volume 56 (2007) issue 5. - page 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 volume 271 (2007) issue 2. - page 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 volume 24 (2007) issue 7. - page 1809-1832
doi:10.1088/0264-9381/24/7/008 ...

Firt, Roman; Rein, Gerhard
Stability of disk-like galaxies : Part I: Stability via reduction
in Analysis volume 26 (2007) issue 4. - page 507-525
doi:10.1524/anly.2006.26.4.507 ...

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 volume 266 (2006) issue 1. - page 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 volume 23 (2006) issue 11. - page 3659-3677
doi:10.1088/0264-9381/23/11/001 ...

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 volume 138 (2005) issue 3. - page 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 volume 1045 (2005) . - page 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 volume 2005 (2005) issue 1. - page 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 volume 204 (2004) issue 2. - page 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 volume 2 (2004) issue 2. - page 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 volume 137 (2004) issue 1. - page 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 volume 52 (2003) issue 4. - page 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 volume 238 (2003) issue 1-2. - page 367-378
doi:10.1007/s00220-003-0861-1 ...

Rein, Gerhard
Non-linear stability of gaseous stars
in Archive for Rational Mechanics and Analysis volume 168 (2003) issue 2. - page 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 volume 28 (2003) issue 11-12. - page 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 volume 134 (2003) issue 3. - page 529-549
doi:10.1017/S0305004102006606 ...

Guo, Yan; Rein, Gerhard
Stable models of elliptical galaxies
in Monthly Notices of the Royal Astronomical Society volume 344 (2003) issue 4. - page 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 volume 106 (2002) issue 5-6. - page 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 volume 33 (2002) issue 4. - page 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 volume 161 (2002) issue 1. - page 27-42
doi:10.1007/s002050100167 ...

2001

Guo, Yan; Rein, Gerhard
Isotropic steady states in galactic dynamics
in Communications in Mathematical Physics volume 219 (2001) . - page 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 volume 11 (2001) issue 3. - page 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 volume 128 (2000) issue 2. - page 363-380

Rein, Gerhard
Stationary and static stellar dynamic models with axial symmetry
in Nonlinear Analysis : Theory, Methods & Applications volume 41 (2000) issue 3-4. - page 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 volume 48 (1999) issue 4. - page 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 volume 205 (1999) issue 1. - page 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 volume 59 (1999) issue 3. - page 831-844
doi:10.1137/S0036139997329069 ...

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

Rein, Gerhard
Static shells for the Vlasov-Poisson and Vlasov-Einstein systems
in Indiana University Mathematics Journal volume 48 (1999) issue 1. - page 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 volume 58 (1998) . - page 044007
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 volume 191 (1998) issue 1. - page 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 volume 3 (1998) issue 2. - page 271-292

1997

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

Rein, Gerhard
Selfgravitating systems in Newtonian theory : the Vlasov-Poisson system
in Banach Center Publications volume 41 (1997) issue 1. - page 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 volume 119 (1996) issue 4. - page 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 volume 176 (1996) issue 2. - page 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 volume 19 (1996) issue 17. - page 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 volume 130 (1995) issue 2. - page 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 volume 168 (1995) issue 3. - page 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 volume 126 (1994) issue 2. - page 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 volume 17 (1994) issue 14. - page 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 volume 115 (1994) issue 3. - page 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 volume 164 (1993) issue 1. - page 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 volume 59 (1993) issue 4. - page 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 volume 15 (1992) issue 5. - page 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 volume 99 (1992) issue 1. - page 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 volume 150 (1992) issue 3. - page 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 volume 150 (1992) issue 3. - page 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 volume 121 (1992) issue 2. - page 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. Série I volume 313 (1991) . - page 411-416

1990

Rein, Gerhard
Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics
in Communications in Mathematical Physics volume 135 (1990) issue 1. - page 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 volume 13 (1990) issue 2. - page 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 volume 4 (1987) issue 1-2. - page 91-103
doi:10.1016/0167-8396(87)90027-6 ...

Prof. Dr. Gerhard Rein

Fakultät für Mathematik, Physik und Informatik
Mathematisches Institut


Prof. Dr. Gerhard Rein
Professor

Chair of Mathematics VI
Building NW II
Room 3.2.01.539
Universität Bayreuth    
95440 Bayreuth   

Phone: 0921/55-3287
E-mail: Gerhard.Rein@uni-bayreuth.de

Office hours by appointment

Webmaster: Univ.Prof.Dr. Gerhard Rein

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