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Title

Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system

Authors 1

Affiliations

  1. Mathematisches Institut der Universität München, Theresienstr., 39, 80333 München, Germany

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.

Bibliography

  1. C. Bardos and P. Degond, Global existence for the Vlasov Poisson equation in 3 space variables with small initial data, Ann. Inst. Henri Poincaré, Analyse non linéaire 2 (1985), 101-111.
  2. J. Batt, Global symmetric solutions of the initial value problem of stellar dynamics, J. Differential Eqns. 25 (1977), 342-364.
  3. J. Batt, Asymptotic properties of spherically symmetric self-gravitating mass systems for t → ∞, Transport Theory and Statistical Mechanics 16 (1987), 763-778.
  4. J. Batt, W. Faltenbacher, and E. Horst, Stationary spherically symmetric models in stellar dynamics, Arch. Rational Mech. Anal. 93 (1986), 159-183 .
  5. J. Batt, P. Morrison, and G. Rein, Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions, Arch. Rational Mech. Anal. 130 (1995), 163-182.
  6. J. Batt and G. Rein, A rigorous stability result for the Vlasov-Poisson system in three dimensions, Anal. di Mat. Pura ed Appl. 164 (1993), 133-154.
  7. F. Bouchut, Existence and uniqueness of a global smooth solution for the Vlasov-Poisson-Fokker-Planck system in three dimensions, J. Functional Analysis 111 (1993), 239-258.
  8. K. Ganguly and H. Victory, On the convergence of particle methods for multidimensional Vlasov-Poisson systems, SIAM J. Numer. Anal. 26 (1989), 249-288
  9. R. Glassey and J. Schaeffer, On symmetric solutions of the relativistic Vlasov-Poisson system, Commun. Math. Phys. 101 (1985), 459-473.
  10. Y. Guo and W. Strauss, Nonlinear instability of double-humped equilibria, Ann. Inst. Henri Poincaré, Analyse non linéaire 12 (1995), 339-352 .
  11. Y. Guo and W. Strauss, Instability of periodic BGK equilibria, Commun. Pure and Appl. Math. XLVIII (1995), 861-894.
  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.
  13. E. Horst, On the asymptotic growth of the solutions of the Vlasov-Poisson system, Math. Meth. in the Appl. Sci. 16 (1993), 75-85.
  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.
  15. P.-L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. math. 105 (1991), 415-430.
  16. K. Pfaffelmoser, Globale klassische Lösungen des dreidimensionalen Vlasov-Poisson-Systems, Dissertation, München 1989 .
  17. K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Differential Eqns. 95 (1992), 281-303.
  18. M. Reed and B. Simon, Methods of Modern Mathematical Physics II, Academic Press, New York, 1975.
  19. G. Rein, Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics, Commun. Math. Phys. 135 (1990), 41-78.
  20. G. Rein, Nonlinear stability for the Vlasov-Poisson system--the energy-Casimir method, Math. Meth. in the Appl. Sci. 17 (1994), 1129-1140.
  21. G. Rein, Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case, Math. Nachrichten, to appear.
  22. G. Rein, Nonlinear stability of homogeneous models in Newtonian cosmology, Arch. Rational Mech. Anal., to appear.
  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.
  24. J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Commun. Part. Diff. Eqns. 16 (1991), 1313-1335.
  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.
Banach Center Publications
1997/41/1
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Pages:
179-194
Main language of publication
English
Published
1997
Exact and natural sciences