@article{RSMUP_1987__78__125_0,
author = {Marchioro, Carlo and Pagani, Enrico},
title = {Nonlinear stability of a spatially symmetric solution of the relativistic {Poisson-Vlasov} equation},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
pages = {125--143},
publisher = {Seminario Matematico of the University of Padua},
volume = {78},
year = {1987},
mrnumber = {934510},
zbl = {0649.35007},
language = {en},
url = {http://archive.numdam.org/item/RSMUP_1987__78__125_0/}
}
TY - JOUR AU - Marchioro, Carlo AU - Pagani, Enrico TI - Nonlinear stability of a spatially symmetric solution of the relativistic Poisson-Vlasov equation JO - Rendiconti del Seminario Matematico della Università di Padova PY - 1987 SP - 125 EP - 143 VL - 78 PB - Seminario Matematico of the University of Padua UR - http://archive.numdam.org/item/RSMUP_1987__78__125_0/ LA - en ID - RSMUP_1987__78__125_0 ER -
%0 Journal Article %A Marchioro, Carlo %A Pagani, Enrico %T Nonlinear stability of a spatially symmetric solution of the relativistic Poisson-Vlasov equation %J Rendiconti del Seminario Matematico della Università di Padova %D 1987 %P 125-143 %V 78 %I Seminario Matematico of the University of Padua %U http://archive.numdam.org/item/RSMUP_1987__78__125_0/ %G en %F RSMUP_1987__78__125_0
Marchioro, Carlo; Pagani, Enrico. Nonlinear stability of a spatially symmetric solution of the relativistic Poisson-Vlasov equation. Rendiconti del Seminario Matematico della Università di Padova, Tome 78 (1987), pp. 125-143. http://archive.numdam.org/item/RSMUP_1987__78__125_0/
[1] , Global existence of a weak solution of Vlasov's system of equations, U.R.S.S. Comput. Math. and Math. Phys., 15 (1) (1975), pp. 131-143. | MR
[2] , Existence and uniqueness of the classical solutions of Vlasov's system of equations, U.R.S.S. Comput. Math. and Math. Phys., 15 (5) (1975), pp. 252-258. | MR | Zbl
[3] - , Global existence for the Vlasov-Poisson equation in three space variables with small initial data, C. R. Acad. Sc. Paris, 297, Sez. 1 (1983), p. 131. | MR
[4] , Global symmetric solutions of the initial-value problem in stellar dynamics, J. Diff. Eq., 25 (1977), pp. 342-364. | MR | Zbl
[5] , The nonlinear Vlasov-Poisson system of partial differential equations in stellar dynamics, Publ. C.N.E.R. Math. Pures Appl. Année 83, vol. 5, fasc. 2 (1983), pp. 1-30.
[6] , Galerkin approximations for the one-dimensional Vlasov-Poisson equation, Math. Meth. in the Appl. Sci., 5 (1983), pp. 516-529. | MR | Zbl
[7] - , Boundary value problem for the Vlasov-Xaxwell equations in one dimension, J. Math. Anal. Appl., 75 (1980), pp. 306-329. | MR | Zbl
[8] - - , Relativistic Kinetic Theory. Principles and Application, North Holland, Amsterdam (1980). | MR
[9] , Bound on the energy available from a plasma, Phys. Fluids, 6 (1963), pp. 839-840. | MR
[10] - J. SCHAEFFER, On symmetric solutions of the relativistic Vlasov-Poisson system, Comm. Math. Phys., 101 (1985), pp. 459-473. | MR | Zbl
[11] - , Singularity formation in a collisionless plasma could occurr only at high velocities, Arch. Rat. Mech. Anal. (in print). | Zbl
[12] - - - , Nonlinear stability of fluid and plasma equilibria, Physics Reports, 123 (1985), pp. 1-116. | MR | Zbl
[13] , On the classical solutions of the initial-value problem for the unmodified nonlinear Vlasov equation I, II, Math. Meth. Appl. Sci., 3 (1981), pp. 229-248; 4 (1982), pp. 19-32. | Zbl
[14] - , Weak solution of the initial-value problem for the unmodified nonlinear Vlasov equation, Math. Meth. Appl. Sci., 6 (1984), pp. 262-279. | MR | Zbl
[15] - , An existence theorem for the unmodified Vlasov equation, Math. Meth. Appl. Sci., 1 (1979), pp. 530-554. | MR | Zbl
[16] - M. PULVIRENTI, Some considerations on the nonlinear stability of stationary planar Euler flows, Comm. Math. Phys., 100 (1985). pp. 343-354. | MR | Zbl
[17] - , A note on the nonlinear stability of a spatial symmetric Vlasov-Poisson flow, Math. Meth. Appl. Sci. (in print). | MR | Zbl
[18] - , The Hamiltonian structure of the Maxwell-Vlasov equations, Physica, 4D (1982), pp. 394-406. | MR
[19] , An introduction to the nonlinear Boltzmann-Vlasov equation, Lecture Notes in Mathematics, 1048 (Springer-Verlag, Berlin, 1984), pp. 60-110. | MR | Zbl
[20] , Approximation methods for the nonmodified Vlasov-Poisson system, Proceedings of the « Workshop on Math. Aspects of Fluid and Plasma Dynamics » (Trieste, Italy, May 30 - June 2, 1984), edited by C. Cercignani, S. Rionero, M. Tessarotto, pp. 439-455.
[21] , Topics in microinstabilities, in Advanced Plasma Physics, M. Rosenbluth, ed. (Academic Press, New York, 1964). | MR
[22] - T. OKABE, On classical solutions in the large in time of two dimensional Vlasov's equation, Osaka J. Math., 15 (1978), pp. 245-261. | MR | Zbl
[23] - , Theoretical Methods in Plasma Physics, North Holland, Amsterdam (1967). | Zbl
[24] , L'equation de Vlasov dans la théorie spéciale de la relativité, Plasma Phys., 9 (1967), pp. 665-670.
[25] , The spherically symmetric Vlasov-Poisson system, J. Diff. Equations, 35 (1980), pp. 30-35. | MR | Zbl
[26] , An existence and uniqueness theorem for the Vlasov-Maxwell system, Commun. Pure Appl. Math., 37 (1984), pp. 457-462. | MR | Zbl
[27] , Global in time solutions of the two dimensional Vlasov-Poisson system, Commun. Pure Appl. Math., 33 (1980), pp. 173-197. | MR | Zbl
[28] , Local existence of solutions of the Maxwell-Vlasov equation and convergence to the Vlasov-Poisson equation for infinite light velocity, Int. Rep. 117, Centre de Mathématiques Appliquées, École Polytéchnique, Paris (1984).
[29] , The classical limit of the relativistic Vlasov-Maxwell system, Commun. Math. Phys., 104 (1986), pp. 403-421. | MR | Zbl
