@article{AIHPC_1999__16_4_503_0,
author = {Castella, F.},
title = {Propagation of space moments in the {Vlasov-Poisson} equation and further results},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {503--533},
year = {1999},
publisher = {Gauthier-Villars},
volume = {16},
number = {4},
mrnumber = {1697563},
zbl = {1011.35034},
language = {en},
url = {https://www.numdam.org/item/AIHPC_1999__16_4_503_0/}
}
TY - JOUR AU - Castella, F. TI - Propagation of space moments in the Vlasov-Poisson equation and further results JO - Annales de l'I.H.P. Analyse non linéaire PY - 1999 SP - 503 EP - 533 VL - 16 IS - 4 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPC_1999__16_4_503_0/ LA - en ID - AIHPC_1999__16_4_503_0 ER -
Castella, F. Propagation of space moments in the Vlasov-Poisson equation and further results. Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) no. 4, pp. 503-533. https://www.numdam.org/item/AIHPC_1999__16_4_503_0/
[1] , Global existence of a weak solution of Vlasov's system of equations, U.S.S.R. Comput. Math. Phys., Vol. 15, 1975, pp. 131-143. | MR
[2] , Some estimates for the solution of the Vlasov equation, (Russian) Zh. Vychiol. Mat. i Mat. Fiz., Vol. 25, No. 1, 1985, pp. 80-87. | MR
[3] , Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation, J. Math. Phys., Vol. 25, No. 11, 1984, pp. 3270-3273. | Zbl | MR
[4] , L2 Solutions to the Schrödinger-Poisson System : Existence, Uniqueness, Time Behaviour, and Smoothing Effects, to appear in Math. Meth. Mod. Appl. Sci., 1997. | Zbl | MR
[5] and , Estimations de Strichartz pour les Equations de Transport Cinétique, C. R. Acad. Sci. Paris, Vol. 322, 1996, pp. 535-540. | Zbl | MR
[6] , An introduction to nonlinear Schrödinger Equations, Second Edition, Textos de Métodos Matemàticas 26, Universidade Federal do Rio de Janeiro, 1993.
[7] and , Solutions globales d'équations du type Vlasov-Poisson, C. R. Acad. Sci. Paris, Vol. 307, 1988, pp. 655-658. | Zbl | MR
[8] and , Global weak solutions of Vlasov-Maxwell Systems, Comm. Pure Appl. Math., Vol. 42, 1989, pp. 729-757. | Zbl | MR
[9] , and , Un résultat de compacité pour les équations de transport, C. R. Acad. Sci. Paris, Série I, Vol. 301, 1985, pp. 341-344. | Zbl | MR
[10] , , and , Regularity of the moments of the solution of a transport equation, J. Funct. Anal., Vol. 76, 1988, pp. 110-125. | Zbl | MR
[11] and , Weak solutions of the initial value problem for the unmodified nonlinear Vlasov equation, Math. Meth. Appl. Sci., Vol. 6, 1984, pp. 262-279. | Zbl | MR
[12] and , Lower Bounds for order of Decay or of Growth in Time for Solutions to Linear and Nonlinear Schrödinger Equations, Publ. RIMS, Kyoto University, Vol. 25, 1989, pp. 847-859. | Zbl | MR
[13] and , An existence theorem for the unmodified Vlasov equation, Math. Meth. Appl. Sci., Vol. 1, 1979, pp. 530-540. | Zbl | MR
[14] and , Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case, to appear in Math. Meth. Appl. Sci. | Zbl | MR
[15] and , Sur les mesures de Wigner, Rev. Mat. Iberoam., Vol. 9, No. 3, 1993, pp. 553-618. | Zbl | MR | EuDML
[16] and , Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., Vol. 105, 1991, pp. 415-430. | Zbl | MR | EuDML
[17] and , Lemmes de moments, de moyenne et de dispersion, C. R. Acad. Sci. Paris, Vol. 314, 1992, pp. 801-806. | Zbl | MR
[18] and , Solutions of the Boltzmann equation with infinite energy, to appear in SIAM J. Math. Anal. | MR
[19] , Time decay, Propagation of Low Moments and Dispersive Effects for Kinetic Equations, Comm. PDE, Vol. 21, 1996, pp. 659-686. | Zbl | MR
[20] , Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Eq., Vol. 95, 1992, pp. 281-303. | Zbl | MR
[21] , Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case, to appear in Math. Nachrichten. | Zbl | MR
[22] , Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system, to appear in Banach Center Publ. | Zbl | MR | EuDML
[23] , Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. PDE., Vol. 16, N. 8-9, 1991, pp. 1313-1335. | Zbl | MR
[24] , Singular integrals and differentiability properties of functions, Princeton University Press, Princeton Mathematical Series 30, 1970. | Zbl | MR





