On the Plasma-Charge problem

Mario Pulvirenti[1]

  • [1] Dipartimento di Matematica “G. Castelnuovo” Università di Roma “La Sapienza” Italy

Séminaire Équations aux dérivées partielles (2009-2010)

  • Volume: 2009-2010, page 1-9

Abstract

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This short report is a review on recent results of S. Caprino, C. Marchioro, E. Miot and the author on the initial value problem associated to the evolution of a continuous distribution of charges (plasma) in presence of a finite number of point charges.

How to cite

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Pulvirenti, Mario. "On the Plasma-Charge problem." Séminaire Équations aux dérivées partielles 2009-2010 (2009-2010): 1-9. <http://eudml.org/doc/116438>.

@article{Pulvirenti2009-2010,
abstract = {This short report is a review on recent results of S. Caprino, C. Marchioro, E. Miot and the author on the initial value problem associated to the evolution of a continuous distribution of charges (plasma) in presence of a finite number of point charges.},
affiliation = {Dipartimento di Matematica “G. Castelnuovo” Università di Roma “La Sapienza” Italy},
author = {Pulvirenti, Mario},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {plasma-charge problem; modified Vlasov-Poisson equation; existence/uniqueness},
language = {eng},
pages = {1-9},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {On the Plasma-Charge problem},
url = {http://eudml.org/doc/116438},
volume = {2009-2010},
year = {2009-2010},
}

TY - JOUR
AU - Pulvirenti, Mario
TI - On the Plasma-Charge problem
JO - Séminaire Équations aux dérivées partielles
PY - 2009-2010
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2009-2010
SP - 1
EP - 9
AB - This short report is a review on recent results of S. Caprino, C. Marchioro, E. Miot and the author on the initial value problem associated to the evolution of a continuous distribution of charges (plasma) in presence of a finite number of point charges.
LA - eng
KW - plasma-charge problem; modified Vlasov-Poisson equation; existence/uniqueness
UR - http://eudml.org/doc/116438
ER -

References

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  1. S. Caprino and C. Marchioro, On the plasma-charge model, Kinetic and Related Models 3 (2010), no. 2, 241-254 (2010). Zbl1193.82045MR2646058
  2. S. Caprino and C. Marchioro, , E. Miot and M. Pulvirenti, In preparation 
  3. T. Glassey, The Cauchy problem in kinetic theory, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1996. Zbl0858.76001MR1379589
  4. E. Horst, On the asymptotic growth of the solutions of the Vlasov-Poisson system, Math. Methods Appl. Sci. 16 (1993), no. 2, 75-86. Zbl0782.35079MR1200156
  5. P.-L. Lions and B. Perthame, Propagation of moments and regularity for the 3 -dimensional Vlasov-Poisson system, Invent. Math. 105 (1991), no. 2, 415-430. Zbl0741.35061MR1115549
  6. C. Marchioro, E. Miot and M. Pulvirenti, The Cauchy problem for the 3-D Vlasov-Poisson system with point charges, preprint (2010) Zbl1321.76081MR2807132
  7. S. Okabe and T. Ukai, On classical solutions in the large in time of the two-dimensional Vlasov equation, Osaka J. Math. 15 (1978), 245-261. Zbl0405.35002MR504289
  8. K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, Jour. Diff. Eq. 95 (1992), 281-303. Zbl0810.35089MR1165424
  9. J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. Partial Differential Equations 16 (1991), no. 8-9, 1313-1335. Zbl0746.35050MR1132787
  10. S. Wollman, Global in time solution to the three-dimensional Vlasov-Poisson system, Jour. Math. Anal. Appl. 176 (1) (1996), 76-81. Zbl0814.35105MR1222156

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