Gerhard Rein

List of publications

in reverse chronological order

• (with Hakan Andreasson , Markus Kunze),
  Rotating, stationary, axially symmetric spacetimes with collisionless matter.
  Preprint, arXiv: 1212.5028 (2012)
  

• (with Mahir Hadzic ),
  Stability for the spherically symmetric Einstein-Vlasov system - a coercivity estimate .
  Preprint, arXiv: 1205.6198 (2012)
  

• (with Tobias Ramming ),
  Spherically symmetric equilibria for self-gravitating
  kinetic or fluid models in the non-relativistic and
  relativistic case---A simple proof for finite extension.
  SIAM Journal on Mathematical Analysis, 45, 900-914 (2013)
  original publication DOI No: 10.1137/120896712

• (with Hakan Andreasson , Markus Kunze),
  Existence of axially symmetric static solutions of the Einstein-Vlasov system
  Commun. Math. Phys., 308, 23-47 (2011)
  original publication DOI No: 10.1007/s00220-011-1324-8

• (with Hakan Andreasson ),
  Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system.
  J. Hyperbolic Differential Eqns. 7, 707-731 (2010)
  original publication DOI No: 10.1142/S0219891610002268

• (with Hakan Andreasson , Markus Kunze),
  The formation of black holes in spherically symmetric gravitational collapse.
  Mathematische Annalen, 350, 683-705 (2011)
  original publication DOI: 10.1007/s00208-010-0578-3.

• (with Hakan Andreasson),
  The asymptotic behaviour in Schwarzschild time of Vlasov matter in spherically symmetric gravitational collapse.
  Math. Proc. Camb. Phil. Soc. 149 (2010), 173-188
  original publication DOI: 10.1017/S0305004109990454

• (with Hakan Andreasson , Markus Kunze),
  Gravitational collapse and the formation of black holes for the spherically symmetric Einstein-Vlasov system.
  Quarterly of Applied Math. LXVIII (2010), 17-42

• (with Hakan Andreasson), Mikael Eklund
  A numerical investigation of the steady states of the spherically symmetric Einstein-Vlasov-Maxwell system.
  Class. Quantum Grav. 26 (2009) 145003 (20pp)
  original publication DOI: 10.1088/0264-9381/26/14/145003

• (with Roman Firt, Martin Seehafer)
  Flat galaxies with dark matter halos - existence and stability.
  Commun. Math. Phys. 291 (2009) 225 - 255
  original publication DOI: 10.1007/s00220-009-0872-7

• (with Hakan Andreasson , Markus Kunze),
  Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter .
  Commun. Partial Differential Eqns. 33, 656-668 (2008)
  original publication DOI: 10.1080/03605300701454883

• (with Mahir Hadzic)
  Global existence and nonlinear stability for the relativistic Vlasov-Poisson system in the gravitational case ,
  Indiana Univ. Math. J. 56, 2453-2488 (2007)
  The original publication is available here.

• (with Hakan Andreasson )
  On the steady states of the spherically symmetric Einstein-Vlasov system .
  Class. Quantum Grav. 24, 1809-1832 (2007)

• (with Yan Guo )
  A non-variational approach to nonlinear stability in stellar dynamics applied to the King model ,
  Commun. Math. Phys. 271, 489-509 (2007)
  original publication DOI: 10.1007/s00220-007-0212-8

• Collisionless Kinetic Equations from Astrophysics---The Vlasov-Poisson System.
  Handbook of Differential Equations, Evolutionary Equations. Vol. 3.
  Eds. C.M. Dafermos and E. Feireisl, Elsevier (2007)

• (with Roman Firt)
  Stability of disk-like galaxies---Part I: Stability via reduction ,
  Analysis 26, 507-525 (2006)
  DOI: 10.1524/anly.2006.26.4.507

• (with Hakan Andreasson )
  A numerical investigation of the stability of steady states and critical phenomena
  for the spherically symmetric Einstein-Vlasov system .
  Class. Quantum Grav. 23 (2006) 3659-3677

• (with S. Bauer, M. Kunze, A. D. Rendall )
  Multipole Radiation in a Collisionless Gas Coupled to Electromagnetism or Scalar Gravitation,
  Commun. Math. Phys. 266, 267-288 (2006)
  The original publication is available at http://dx.doi.org/10.1007/s00220-006-0015-3

• (with Michael Kunzinger , Roland Steinbauer , Gerald Teschl )
  On classical solutions of the relativistic Vlasov-Klein-Gordon system,
  Electronic Journal of Diff. Eqns. No 1, Vol. 2005, 1 - 17 (2005)

• (with Hakan Andreasson and Simone Calogero )
  Global classical solutions to the spherically symmetric Nordström-Vlasov system,
  Math. Proc. Camb. Phil. Soc. 138, 533 - 539 (2005)
  Digital Object Identifier (DOI) 10.1017/S0305004105008467

• (with Simone Calogero )
  Global weak solutions to the Nordström-Vlasov system,
  Journal of Differential Equations, Vol. 204, 323 - 338 (2004)

• Global weak solutions to the relativistic Vlasov-Maxwell system revisited,
  Commun. Math. Sci. Vol. 2, No. 2, 145 - 158 (2004)
  

• On future geodesic completeness for the Einstein-Vlasov system with hyperbolic symmetry,
  Math. Proc. Camb. Phil. Soc. 137, 237 - 244 (2004)
  

• (with Simone Calogero )
  On classical solutions of the Nordström-Vlasov system,
  Commun. Partial Differential Eqns. 28, 1863 - 1885 (2003)

• Non-linear stability of gaseous stars,
  Arch. Rational Mech. Anal. 168, 115 - 130 (2003)
  The original publication is available at http://link.springer.de
  Digital Object Identifier (DOI) 10.1007/s00205-003-0260-y

• (with Michael Kunzinger , Roland Steinbauer , Gerald Teschl )
  Global weak solutions of the relativistic Vlasov-Klein-Gordon system,
  Commun. Math. Phys. 238, 367-378 (2003)
  The original publication is available at http://link.springer.de
  DOI 10.1007/s00220-003-0861-1

• (with Yan Guo )
  Stable models of elliptical galaxies ,
  Mon. Not. R. Astron. Soc. 344, 1296 -1306 (2003)

• (with Thomas Rodewis)
  Convergence of a particle-in-cell scheme for the spherically symmetric Vlasov-Einstein system,
  Indiana University Mathematics Journal 52, 821 - 862 (2003)
  The original publication is available here.

• (with Hakan Andreasson ) and A. D. Rendall )
  On the Einstein-Vlasov system with hyperbolic symmetry ,
  Math. Proc. Camb. Phil. Soc., 134, 529 - 549 (2003)

• Reduction and a concentration-compactness principle
  for energy-Casimir functionals ,
  SIAM Journal on Mathematical Analysis, 33, 896 - 912 (2002)

• (with P. Markowich and G. Wolansky)
  Existence and nonlinear stability of steady states
  of the Schrödinger-Poisson system ,
  Journal of Statistical Physics 106 (5/6), 1221-1239 (2002)

• Stability of spherically symmetric steady states in galactic dynamics
  against general perturbations ,
  Arch. Rational Mech. Anal. 161, 27-42 (2002)
  The original publication is available at http://link.springer.de
  Digital Object Identifier (DOI) 10.1007/s0020500100167

• (with Yan Guo )
  Isotropic steady states in galactic dynamics ,
  Commun. Math. Phys, 219, 607 - 629 (2001)

• (with Yan Guo )
  Isotropic steady states in galactic dynamics revised

• (with Jean Dolbeault )
  Time-dependent rescalings and Lyapunov functionals for the Vlasov-Poisson
  and Euler-Poisson systems, and for related models of kinetic equations,
  fluid dynamics and quantum physics ,
  Math. Models Methods Appl. Sci. 11, 407 - 432 (2001)

• Stationary and static stellar dynamic models with axial symmetry ,
  Nonlinear Analysis; Theory, Methods & Applications 41, 313 - 344 (2000)

• (with A. D. Rendall )
  Compact support of spherically symmetric equilibria
  in non-relativistic and relativistic galactic dynamics ,
  Math. Proc. Camb. Phil. Soc. 128, 363-380 (2000)

• (with Yan Guo )
  Existence and stability of Camm type steady states in galactic dynamics ,
  Indiana University Mathematics Journal 48, 1237 - 1255 (1999)

• Static shells for the Vlasov-Poisson and Vlasov-Einstein systems ,
  Indiana University Mathematics Journal 48, 335-346 (1999)

• Flat steady states in stellar dynamics - existence and stability ,
  Commun. Math. Phys. 205, 229-247 (1999)

• (with Yan Guo )
  Stable steady states in stellar dynamics ,
  Arch. Rational Mech. Anal. 147, 225-243 (1999)

• (with P. Braasch, J. Vukadinovic)
  Nonlinear stability of stationary plasmas - an extension
  of the energy-Casimir method ,
  SIAM Journal in Appl. Math. 59, 831-844 (1999)

• (with A. D. Rendall , J. Schaeffer)
  Critical collapse of collisionless matter - a numerical investigation ,
  Physical Reviews D, Vol. 58, article number 044007 (1998)

• (with J. Batt, M. Kunze)
  On the asymptotic behaviour of a one-dimensional, monocharged plasma
  and a rescaling method ,
  Advances in Differential Equations 3, 271-292 (1998)

• Growth estimates for the solutions of the Vlasov-Poisson system
  in the plasma physics case ,
  Math. Nachrichten 191, 269-278 (1998)

• Selfgravitating systems in Newtonian theory-the Vlasov-Poisson system ,
  Proceedings of the Minisemester on Mathematical Aspects of Theories of Gravitation 1996,
  Banach Center Publications 41, part I, 179--194 (1997)

• Nonlinear stability of homogeneous models in Newtonian cosmology ,
  Arch. Rational Mech. Anal. 140, 335-351 (1997)

• (with R. Illner)
  Time decay of the solutions of the Vlasov-Poisson system
  in the plasma physical case ,
  Math. Meth. in the Appl. Sci. 19, 1409-1413 (1996)

• Cosmological solutions of the Vlasov-Einstein system
  with spherical, plane, or hyperbolic symmetry ,
  Math. Proc. Camb. Phil. Soc. 119, 739-762 (1996)

• The Vlasov-Einstein system with surface symmetry ,
  Habilitationsschrift, München 1995

• (with J. Batt, P. J. Morrison)
  Linear stability of stationary solutions of the Vlasov-Poisson system
  in three dimensions ,
  Arch. Rational Mech. Anal. 130, 163-182 (1995)

• (with A. D. Rendall , J. Schaeffer)
  A regularity theorem for the spherically symmetric
  Vlasov-Einstein system ,
  Commun. Math. Phys. 168, 467-478 (1995)

• Nonlinear stability for the Vlasov-Poisson system-
  the energy-Casimir method ,
  Math. Meth. in the Appl. Sci. 17, 1129-1140 (1994)
  ( abstract )

• (with A. D. Rendall )
  Global existence of classical solutions to the Vlasov-Poisson system
  in a three-dimensional, cosmological setting ,
  Arch. Rational Mech. Anal. 126, 183-201 (1994)
  ( abstract )

• Static solutions of the spherically symmetric Vlasov-Einstein system ,
  Math. Proc. Camb. Phil. Soc. 115, 559-570 (1994)
  ( abstract )

• (with A. D. Rendall )
  Smooth static solutions of the spherically symmetric
  Vlasov-Einstein system,
  Ann. de l'Inst. H. Poincaré, Physique Théorique 59, 383-397 (1993)
  ( abstract )

• (with J. Batt )
  A rigorous stability result for the Vlasov-Poisson system
  in three dimensions,
  Anal. di Mat. Pura ed Appl. 164, 133-154 (1993)
  ( abstract )

• (with A. D. Rendall )
  The Newtonian limit of the spherically symmetric
  Vlasov-Einstein system,
  Commun. Math. Phys. 150, 585-591 (1992)
  ( abstract )

• (with A. D. Rendall )
  Global existence of solutions of the spherically symmetric
  Vlasov-Einstein system with small initial data,
  Commun. Math. Phys. 150, 561-583 (1992)
  ( abstract )
  Erratum: Commun. Math. Phys. 176, 475-478 (1996)
  ( abstract )

• Existence of stationary, collisionless plasmas on bounded domains,
  Math. Meth. in the Appl. Sci. 15, 365-374 (1992)
  ( abstract )

• (with K.-O. Kruse)
  A stability result for the relativistic Vlasov-Maxwell system,
  Arch. Rational Mech. Anal. 121, 187-203 (1992)
  ( abstract )

• (with J. Weckler)
  Generic global solutions of the Vlasov-Fokker-Planck-Poisson
  system in three dimensions,
  J. Differential Eqns. 99, 59-77 (1992)
  ( abstract )

• (with J. Batt )
  Global classical solutions of the periodic Vlasov-Poisson system in three dimensions,
  C. R. Acad. Sc. Paris 313, 411-416 (1991)
  ( abstract )

• Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics,
  Commun. Math. Phys. 135, 41-78 (1990)
  ( abstract )

• A two-species plasma in the limit of large ion mass,
  Math. Meth. in the Appl. Sci. 13, 159-167 (1990)
  ( abstract )

• (with G. Farin, N. Sapidis, A. J. Worsey)
  Fairing cubic b-spline curves,
  Computer Aided Geometric Design 4, 91-103 (1987)
  ( abstract )