On the Plasma-Charge problem
Pulvirenti, Mario1
1 Dipartimento di Matematica “G. Castelnuovo” Università di Roma “La Sapienza” Italy
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 
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Pulvirenti, Mario. On the Plasma-Charge problem. Séminaire Goulaouic-Schwartz (2009-2010), Exposé no. 14, 9 p.. https://www.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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR | EuDML

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

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