Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system

Gerhard Rein

Banach Center Publications (1997)

  • Volume: 41, Issue: 1, page 179-194
  • ISSN: 0137-6934

Abstract

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We give a review of results on the initial value problem for the Vlasov--Poisson system, concentrating on the main ingredients in the proof of global existence of classical solutions.

How to cite

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Rein, Gerhard. "Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system." Banach Center Publications 41.1 (1997): 179-194. <http://eudml.org/doc/252246>.

@article{Rein1997,
abstract = {We give a review of results on the initial value problem for the Vlasov--Poisson system, concentrating on the main ingredients in the proof of global existence of classical solutions.},
author = {Rein, Gerhard},
journal = {Banach Center Publications},
keywords = {Vlasov-Poisson system; global existence},
language = {eng},
number = {1},
pages = {179-194},
title = {Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system},
url = {http://eudml.org/doc/252246},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Rein, Gerhard
TI - Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system
JO - Banach Center Publications
PY - 1997
VL - 41
IS - 1
SP - 179
EP - 194
AB - We give a review of results on the initial value problem for the Vlasov--Poisson system, concentrating on the main ingredients in the proof of global existence of classical solutions.
LA - eng
KW - Vlasov-Poisson system; global existence
UR - http://eudml.org/doc/252246
ER -

References

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  10. [10] Y. Guo and W. Strauss, Nonlinear instability of double-humped equilibria, Ann. Inst. Henri Poincaré, Analyse non linéaire 12 (1995), 339-352 . Zbl0836.35130
  11. [11] Y. Guo and W. Strauss, Instability of periodic BGK equilibria, Commun. Pure and Appl. Math. XLVIII (1995), 861-894. Zbl0840.45012
  12. [12] E. Horst, On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation II, Math. Meth. in the Appl. Sci. 4 (1982), 19-32. Zbl0485.35079
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  14. [14] R. Illner and G. Rein, Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case, Math. Meth. in the Appl. Sci. 19 (1996), 1409-1413. Zbl0872.35087
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  18. [18] M. Reed and B. Simon, Methods of Modern Mathematical Physics II, Academic Press, New York, 1975. Zbl0308.47002
  19. [19] G. Rein, Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics, Commun. Math. Phys. 135 (1990), 41-78. Zbl0722.35091
  20. [20] G. Rein, Nonlinear stability for the Vlasov-Poisson system--the energy-Casimir method, Math. Meth. in the Appl. Sci. 17 (1994), 1129-1140. Zbl0814.76094
  21. [21] G. Rein, Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case, Math. Nachrichten, to appear. 
  22. [22] G. Rein, Nonlinear stability of homogeneous models in Newtonian cosmology, Arch. Rational Mech. Anal., to appear. 
  23. [23] G. Rein and A. Rendall, Global existence of classical solutions to the Vlasov-Poisson system in a three-dimensional, cosmological setting, Arch. Rational Mech. Anal. 126 (1994), 183-201. Zbl0808.35109
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  25. [25] J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions (`The Good, the Bad, and the Ugly'), unpublished manuscript. 

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