Propagation of space moments in the Vlasov-Poisson equation and further results
Castella, F.
Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999), p. 503-533 / Harvested from Numdam
@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},
     volume = {16},
     year = {1999},
     pages = {503-533},
     mrnumber = {1697563},
     zbl = {1011.35034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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, Tome 16 (1999) pp. 503-533. http://gdmltest.u-ga.fr/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 371322

[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 779275

[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 761850 | Zbl 0554.35123

[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 1487521 | Zbl 0892.35141

[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 1383431 | Zbl 0848.35095

[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 967806 | Zbl 0682.35022

[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 1003433 | Zbl 0698.35128

[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 808622 | Zbl 0591.45007

[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 923047 | Zbl 0652.47031

[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 751745 | Zbl 0556.35022

[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 1045995 | Zbl 0714.35014

[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 548686 | Zbl 0415.35076

[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 1414402 | Zbl 0872.35087

[15] P.L. Lions and Th. Paul, Sur les mesures de Wigner, Rev. Mat. Iberoam., Vol. 9, No. 3, 1993, pp. 553-618. | MR 1251718 | Zbl 0801.35117

[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. | MR 1115549 | Zbl 0741.35061

[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 1166050 | Zbl 0761.35085

[18] B. Perthame and S. Mischler, Solutions of the Boltzmann equation with infinite energy, to appear in SIAM J. Math. Anal. | MR 1466666

[19] B. Perthame, Time decay, Propagation of Low Moments and Dispersive Effects for Kinetic Equations, Comm. PDE, Vol. 21, 1996, pp. 659-686. | MR 1387464 | Zbl 0852.35139

[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 1165424 | Zbl 0810.35089

[21] G. Rein, Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case, to appear in Math. Nachrichten. | MR 1621318 | Zbl 0937.76096

[22] G. Rein, Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system, to appear in Banach Center Publ. | MR 1466518 | Zbl 0893.35130

[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 1132787 | Zbl 0746.35050

[24] E.M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, Princeton Mathematical Series 30, 1970. | MR 290095 | Zbl 0207.13501