On the Plasma-Charge problem
Pulvirenti, Mario1
1 Dipartimento di Matematica “G. Castelnuovo” Università di Roma “La Sapienza” Italy
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2009-2010), Exposé no. 14, 9 p.

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.

Pulvirenti, Mario 1

1 Dipartimento di Matematica “G. Castelnuovo” Università di Roma “La Sapienza” Italy 
@article{SEDP_2009-2010____A14_0,
     author = {Pulvirenti, Mario},
     title = {On the {Plasma-Charge} problem},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:14},
     pages = {1--9},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2009-2010},
     mrnumber = {3098625},
     language = {en},
     url = {http://archive.numdam.org/item/SEDP_2009-2010____A14_0/}
}
TY  - JOUR
AU  - Pulvirenti, Mario
TI  - On the Plasma-Charge problem
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:14
PY  - 2009-2010
SP  - 1
EP  - 9
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://archive.numdam.org/item/SEDP_2009-2010____A14_0/
LA  - en
ID  - SEDP_2009-2010____A14_0
ER  - 
%0 Journal Article
%A Pulvirenti, Mario
%T On the Plasma-Charge problem
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:14
%D 2009-2010
%P 1-9
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://archive.numdam.org/item/SEDP_2009-2010____A14_0/
%G en
%F SEDP_2009-2010____A14_0
Pulvirenti, Mario. On the Plasma-Charge problem. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2009-2010), Exposé no. 14, 9 p. http://archive.numdam.org/item/SEDP_2009-2010____A14_0/

[1] S. Caprino and C. Marchioro, On the plasma-charge model, Kinetic and Related Models 3 (2010), no. 2, 241-254 (2010). | MR

[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. | MR | Zbl

[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. | MR | Zbl

[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. | EuDML | MR | Zbl

[6] C. Marchioro, E. Miot and M. Pulvirenti, The Cauchy problem for the 3-D Vlasov-Poisson system with point charges, preprint (2010) | MR

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[10] S. Wollman, Global in time solution to the three-dimensional Vlasov-Poisson system, Jour. Math. Anal. Appl. 176 (1) (1996), 76-81. | MR | Zbl