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) , p. 125-143
Zbl 0649.35007 | MR 934510
URL stable : http://www.numdam.org/item?id=RSMUP_1987__78__125_0

Bibliographie

[1] A.A. Arsen'Ev, 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 371322

[2] A.A. Arsen'Ev, 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 395633 | Zbl 0345.35083

[3] C. Bardos - P. Degond, 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 732496

[4] J. Batt, Global symmetric solutions of the initial-value problem in stellar dynamics, J. Diff. Eq., 25 (1977), pp. 342-364. MR 487082 | Zbl 0366.35020

[5] J. Batt, 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] J. Cooper, Galerkin approximations for the one-dimensional Vlasov-Poisson equation, Math. Meth. in the Appl. Sci., 5 (1983), pp. 516-529. MR 723605 | Zbl 0541.65084

[7] J. Cooper - A. Klimas, Boundary value problem for the Vlasov-Xaxwell equations in one dimension, J. Math. Anal. Appl., 75 (1980), pp. 306-329. MR 581821 | Zbl 0454.35075

[8] S.R. De Groot - C.G. Van Weert - W.A. Van Leeuwen, Relativistic Kinetic Theory. Principles and Application, North Holland, Amsterdam (1980). MR 635279

[9] C.S. Gardner, Bound on the energy available from a plasma, Phys. Fluids, 6 (1963), pp. 839-840. MR 152330

[10] R. Glassey - J. SCHAEFFER, On symmetric solutions of the relativistic Vlasov-Poisson system, Comm. Math. Phys., 101 (1985), pp. 459-473. MR 815195 | Zbl 0582.35110

[11] R. Glassey - W. Strauss, Singularity formation in a collisionless plasma could occurr only at high velocities, Arch. Rat. Mech. Anal. (in print). Zbl 0595.35072

[12] D.D. Holm - J.E. Marsden - T. Ratiu - A. Weinstein, Nonlinear stability of fluid and plasma equilibria, Physics Reports, 123 (1985), pp. 1-116. MR 794110 | Zbl 0717.76051

[13] E. Horst, 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 0463.35071

[14] E. Horst - R. Hunze, Weak solution of the initial-value problem for the unmodified nonlinear Vlasov equation, Math. Meth. Appl. Sci., 6 (1984), pp. 262-279. MR 751745 | Zbl 0556.35022

[15] R. Illner - H. Neunzert, An existence theorem for the unmodified Vlasov equation, Math. Meth. Appl. Sci., 1 (1979), pp. 530-554. MR 548686 | Zbl 0415.35076

[16] C. Marchioro - M. PULVIRENTI, Some considerations on the nonlinear stability of stationary planar Euler flows, Comm. Math. Phys., 100 (1985). pp. 343-354. MR 802550 | Zbl 0625.76060

[17] C. Marchioro - M. Pulvirenti, A note on the nonlinear stability of a spatial symmetric Vlasov-Poisson flow, Math. Meth. Appl. Sci. (in print). MR 845931 | Zbl 0609.35008

[18] J.E. Marsden - A. Weinstein, The Hamiltonian structure of the Maxwell-Vlasov equations, Physica, 4D (1982), pp. 394-406. MR 657741

[19] H. Neunzert, An introduction to the nonlinear Boltzmann-Vlasov equation, Lecture Notes in Mathematics, 1048 (Springer-Verlag, Berlin, 1984), pp. 60-110. MR 740721 | Zbl 0575.76120

[20] H. Neunzert, 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] M.N. Rosenbluth, Topics in microinstabilities, in Advanced Plasma Physics, M. Rosenbluth, ed. (Academic Press, New York, 1964). MR 170672

[22] S. Ukai - 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 504289 | Zbl 0405.35002

[23] N.G. Van Kampen - B.V. Felderhof, Theoretical Methods in Plasma Physics, North Holland, Amsterdam (1967). Zbl 0159.29601

[24] E. Weibel, L'equation de Vlasov dans la théorie spéciale de la relativité, Plasma Phys., 9 (1967), pp. 665-670.

[25] S. Wollman, The spherically symmetric Vlasov-Poisson system, J. Diff. Equations, 35 (1980), pp. 30-35. MR 556789 | Zbl 0402.76089

[26] S. Wollman, An existence and uniqueness theorem for the Vlasov-Maxwell system, Commun. Pure Appl. Math., 37 (1984), pp. 457-462. MR 745326 | Zbl 0592.45010

[27] S. Wollman, Global in time solutions of the two dimensional Vlasov-Poisson system, Commun. Pure Appl. Math., 33 (1980), pp. 173-197. MR 562549 | Zbl 0437.45023

[28] P. Degond, 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] J. Schaeffer, The classical limit of the relativistic Vlasov-Maxwell system, Commun. Math. Phys., 104 (1986), pp. 403-421. MR 840744 | Zbl 0597.35109