Propagation of space moments in the Vlasov-Poisson equation and further results
Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 4, pp. 503-533.
@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},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {4},
     year = {1999},
     mrnumber = {1697563},
     zbl = {1011.35034},
     language = {en},
     url = {http://archive.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  - http://archive.numdam.org/item/AIHPC_1999__16_4_503_0/
LA  - en
ID  - AIHPC_1999__16_4_503_0
ER  - 
%0 Journal Article
%A Castella, F.
%T Propagation of space moments in the Vlasov-Poisson equation and further results
%J Annales de l'I.H.P. Analyse non linéaire
%D 1999
%P 503-533
%V 16
%N 4
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPC_1999__16_4_503_0/
%G en
%F AIHPC_1999__16_4_503_0
Castella, F. Propagation of space moments in the Vlasov-Poisson equation and further results. Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 4, pp. 503-533. http://archive.numdam.org/item/AIHPC_1999__16_4_503_0/

[1] A.A. Arsenev, 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] A.A. Arsenev, 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] J.E. Barab, Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation, J. Math. Phys., Vol. 25, No. 11, 1984, pp. 3270-3273. | MR | Zbl

[4] F. Castella, L2 Solutions to the Schrödinger-Poisson System : Existence, Uniqueness, Time Behaviour, and Smoothing Effects, to appear in Math. Meth. Mod. Appl. Sci., 1997. | MR | Zbl

[5] F. Castella and B. Perthame, Estimations de Strichartz pour les Equations de Transport Cinétique, C. R. Acad. Sci. Paris, Vol. 322, 1996, pp. 535-540. | MR | Zbl

[6] T. Cazenave, An introduction to nonlinear Schrödinger Equations, Second Edition, Textos de Métodos Matemàticas 26, Universidade Federal do Rio de Janeiro, 1993.

[7] R.J. Di Perna and P.L. Lions, Solutions globales d'équations du type Vlasov-Poisson, C. R. Acad. Sci. Paris, Vol. 307, 1988, pp. 655-658. | MR | Zbl

[8] R.J. Di Perna and P.L. Lions, Global weak solutions of Vlasov-Maxwell Systems, Comm. Pure Appl. Math., Vol. 42, 1989, pp. 729-757. | MR | Zbl

[9] F. Golse, B. Perthame and R. Sentis, Un résultat de compacité pour les équations de transport, C. R. Acad. Sci. Paris, Série I, Vol. 301, 1985, pp. 341-344. | MR | Zbl

[10] F. Golse, P.L. Lions, B. Perthame and R. Sentis, Regularity of the moments of the solution of a transport equation, J. Funct. Anal., Vol. 76, 1988, pp. 110-125. | MR | Zbl

[11] E. Horst and R. Hunze, Weak solutions of the initial value problem for the unmodified nonlinear Vlasov equation, Math. Meth. Appl. Sci., Vol. 6, 1984, pp. 262-279. | MR | Zbl

[12] N. Hayashi and T. Ozawa, 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. | MR | Zbl

[13] R. Illner and H. Neunzert, An existence theorem for the unmodified Vlasov equation, Math. Meth. Appl. Sci., Vol. 1, 1979, pp. 530-540. | MR | Zbl

[14] R. Illner and G. Rein, Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case, to appear in Math. Meth. Appl. Sci. | MR | Zbl

[15] P.L. Lions and Th. Paul, Sur les mesures de Wigner, Rev. Mat. Iberoam., Vol. 9, No. 3, 1993, pp. 553-618. | EuDML | MR | Zbl

[16] P.L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., Vol. 105, 1991, pp. 415-430. | EuDML | MR | Zbl

[17] P.L. Lions and B. Perthame, Lemmes de moments, de moyenne et de dispersion, C. R. Acad. Sci. Paris, Vol. 314, 1992, pp. 801-806. | MR | Zbl

[18] B. Perthame and S. Mischler, Solutions of the Boltzmann equation with infinite energy, to appear in SIAM J. Math. Anal. | MR

[19] B. Perthame, Time decay, Propagation of Low Moments and Dispersive Effects for Kinetic Equations, Comm. PDE, Vol. 21, 1996, pp. 659-686. | MR | Zbl

[20] K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Eq., Vol. 95, 1992, pp. 281-303. | MR | Zbl

[21] G. Rein, Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case, to appear in Math. Nachrichten. | MR | Zbl

[22] G. Rein, Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system, to appear in Banach Center Publ. | EuDML | MR | Zbl

[23] J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. PDE., Vol. 16, N. 8-9, 1991, pp. 1313-1335. | MR | Zbl

[24] E.M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, Princeton Mathematical Series 30, 1970. | MR | Zbl