Propagation of space moments in the Vlasov-Poisson Equation and further results

Arsenev, 1975, Global existence of a weak solution of Vlasov's system of equations, U.S.S.R. Comput. Math. Phys., Vol. 15, 131, 10.1016/0041-5553(75)90141-X Arsenev, 1985, Some estimates for the solution of the Vlasov equation, Zh. Vychiol. Mat. i Mat. Fiz., Vol. 25, 80 Barab, 1984, Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation, J. Math. Phys., Vol. 25, 3270, 10.1063/1.526074 Castella, 1997, L2 Solutions to the Schrödinger-Poisson System: Existence, Uniqueness, Time Behaviour, and Smoothing Effects, Math. Meth. Mod. Appl. Sci., 10.1142/S0218202597000530 Castella, 1996, Estimations de Strichartz pour les Equations de Transport Cinétique, C. R. Acad. Sci. Paris, Vol. 322, 535 Cazenave, 1993, An introduction to nonlinear Schrödinger Equations, 26 Di Perna, 1988, Solutions globales d’équations du type Vlasov-Poisson, C. R. Acad. Sci. Paris, Vol. 307, 655 Di Perna, 1989, Global weak solutions of Vlasov-Maxwell Systems, Comm. Pure Appl. Math., Vol. 42, 729, 10.1002/cpa.3160420603 Golse, 1985, Un résultat de compacité pour les équations de transport, C. R. Acad. Sci. Paris, Vol. 301, 341 Golse, 1988, Regularity of the moments of the solution of a transport equation, J. Funct. Anal., Vol. 76, 110, 10.1016/0022-1236(88)90051-1 Horst, 1984, Weak solutions of the initial value problem for the unmodified nonlinear Vlasov equation, Math. Meth. Appl. Sci., Vol. 6, 262, 10.1002/mma.1670060118 Hayashi, 1989, Lower Bounds for order of Decay or of Growth in Time for Solutions to Linear and Nonlinear Schrödinger Equations, Vol. 25, 847 Illner, 1979, An existence theorem for the unmodified Vlasov equation, Math. Meth. Appl. Sci., Vol. 1, 530, 10.1002/mma.1670010410 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. Lions, 1993, Sur les mesures de Wigner, Rev. Mat. Iberoam., Vol. 9, 553, 10.4171/RMI/143 Lions, 1991, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., Vol. 105, 415, 10.1007/BF01232273 Lions, 1992, Lemmes de moments, de moyenne et de dispersion, C. R. Acad. Sci. Paris, Vol. 314, 801 B. Perthame and S. Mischler, Solutions of the Boltzmann equation with infinite energy, to appear in SIAM J. Math. Anal. Perthame, 1996, Time decay, Propagation of Low Moments and Dispersive Effects for Kinetic Equations, Comm. PDE, Vol. 21, 659, 10.1080/03605309608821201 Pfaffelmoser, 1992, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Eq., Vol. 95, 281, 10.1016/0022-0396(92)90033-J G. Rein, Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case, to appear in Math. Nachrichten. G. Rein, Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system, to appear in Banach Center Publ. Schaeffer, 1991, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. PDE., Vol. 16, 1313, 10.1080/03605309108820801 Stein, 1970, Singular integrals and differentiability properties of functions