Voir la notice de l'acte provenant de la source Numdam
Le but de ce texte est de présenter des résultats, en collaboration avec L. Desvillettes et C. Saffirio, à propos de l’existence globale d’une solution pour un système de Vlasov-Poisson avec une charge ponctuelle en dimension trois.
@article{SLSEDP_2013-2014____A1_0,
author = {Miot, Evelyne},
title = {Existence globale et propagation des moments pour une \'equation de {Vlasov-Poisson} avec une charge ponctuelle},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:1},
pages = {1--16},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2013-2014},
doi = {10.5802/slsedp.49},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.5802/slsedp.49/}
}
TY - JOUR AU - Miot, Evelyne TI - Existence globale et propagation des moments pour une équation de Vlasov-Poisson avec une charge ponctuelle JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:1 PY - 2013-2014 SP - 1 EP - 16 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://geodesic.mathdoc.fr/articles/10.5802/slsedp.49/ DO - 10.5802/slsedp.49 LA - fr ID - SLSEDP_2013-2014____A1_0 ER -
%0 Journal Article %A Miot, Evelyne %T Existence globale et propagation des moments pour une équation de Vlasov-Poisson avec une charge ponctuelle %J Séminaire Laurent Schwartz — EDP et applications %Z talk:1 %D 2013-2014 %P 1-16 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U http://geodesic.mathdoc.fr/articles/10.5802/slsedp.49/ %R 10.5802/slsedp.49 %G fr %F SLSEDP_2013-2014____A1_0
Miot, Evelyne. Existence globale et propagation des moments pour une équation de Vlasov-Poisson avec une charge ponctuelle. Séminaire Laurent Schwartz — EDP et applications (2013-2014), Exposé no. 1, 16 p. doi : 10.5802/slsedp.49. http://geodesic.mathdoc.fr/articles/10.5802/slsedp.49/
[1] A. A. Arsenev, Global existence of a weak solution of Vlasov’s system of equations, U. S. S. R. Comput. Math. Math. Phys. 15 (1975), 131–143. | Zbl | MR
[2] C. Bardos et P. Degond, Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data, Ann. Inst. H. Poincaré Anal. Non Linéaire 2, 2 (1985), 101–118. | Zbl | MR | mathdoc-id
[3] J. Batt, Global symmetric solutions of the initial value problem of stellar dynamics, J. Differential Equations 25 (1977), no. 3, 342–364. | Zbl | MR
[4] S. Caprino et C. Marchioro, On the plasma-charge model, Kinet. Relat. Models 3 (2) (2010), 241–254. | Zbl | MR
[5] F. Castella, Propagation of space moments in the Vlasov-Poisson Equation and further results, Ann. Inst. Henri Poincaré 16 (1999), no. 4, 503–533. | Zbl | MR | mathdoc-id
[6] L. Desvillettes, E. Miot et C. Saffirio, Polynomial propagation of moments and global existence for a Vlasov-Poisson system with a point charge, preprint.
[7] R. J. Di Perna et P. L. Lions, Ordinary differential equations, transport equations and Sobolev spaces, Inv. Math. 98 (1989), 511–547. | Zbl | MR
[8] I. Gasser, P. E. Jabin et B. Perthame, Regularity and propagation of moments in some nonlinear Vlasov systems, Proc. Roy. Soc. Edinburgh Sect. A 130 (2000), 1259–1273. | Zbl | MR
[9] R. T. Glassey, The Cauchy problem in kinetic theory, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1996. | Zbl | MR
[10] P. L. Lions et B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math. 105 (1991), 415–430. | Zbl | MR
[11] G. Loeper, Uniqueness of the solution to the Vlasov-Poisson system with bounded density, J. Math. Pures Appl. (9) 86 (2006), no. 1, 68–79. | Zbl | MR
[12] S. Okabe et 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
[13] C. Pallard, Moment propagation for weak solutions to the Vlasov-Poisson system, Commun. Partial Differ. Equations 37 (7) (2012), 1273–1285. | MR
[14] K. Pfaffelmoser, Global existence of the Vlasov-Poisson system in three dimensions for general initial data, J. Differ. Equ. 95 (1992), 281–303. | Zbl | MR
[15] C. Marchioro, E. Miot et M. Pulvirenti, The Cauchy problem for the Vlasov-Poisson system with point charges, Arch. Ration. Mech. Anal. 201 (2011), 1–26. | MR
[16] G. Rein, Collisionless kinetic equations from astrophysic–the Vlasov-Poisson system, Handb. Differ. Equ., Vol. III, 383Ð476, Elsevier/North-Holland, Amsterdam, 2007. | Zbl | MR
[17] D. Salort, Transport equations with unbounded force fields and application to the Vlasov-Poisson equation, Math. Models Methods Appl. Sci. 19 (2) (2009), 199–228. | Zbl | MR
[18] J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Commun. Partial Differ. Equations 16 (8–9) (1991), 1313–1335. | Zbl | MR
[19] S. Wollman, The spherically symmetric Vlasov-Poisson system, J. Differential Equations 35 (1980), no. 1, 30–35. | Zbl | MR
[20] S. Wollman, Global in time solution to the three-dimensional Vlasov-Poisson system, J. Math. Anal. Appl. 176 (1) (1996), 76–91. | Zbl | MR
Cité par Sources :