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Growth estimates and uniform decay for a collisionless plasma
1. | Laboratoire de Mathématiques, Université Paris-Sud 11, 91405 Orsay, France |
References:
[1] |
C. Bardos and P. Degond, Global existence for the Vlasov Poisson equation in $3$ space variables with small initial data, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2 (1985), 101-118. |
[2] |
J. Batt, M. Kunze and G. Rein, On the asymptotic behaviour of a one-dimensional monocharged plasma, Adv. Differential Equations, 3 (1998), 271-292. |
[3] |
R. Glassey, "The Cauchy Problem in Kinetic Theory," SIAM, 1996. |
[4] |
E. Horst, Symmetric plasmas and their decay, Comm. Math. Phys., 126 (1990), 613-633.
doi: 10.1007/BF02125703. |
[5] |
E. Horst, On the asymptotic growth of the solutions of the Vlasov-Poisson system, Math. Meth. Appl. Sci., 16 (1993), 75-85.
doi: 10.1002/mma.1670160202. |
[6] |
R. Illner and G. Rein, Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case, Math. Meth. Appl. Sci., 19 (1996), 1409-1413.
doi: 10.1002/(SICI)1099-1476(19961125)19:17<1409::AID-MMA836>3.0.CO;2-2. |
[7] |
P. L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., 105 (1991), 415-430.
doi: 10.1007/BF01232273. |
[8] |
C. Pallard, A note on the growth of velocities in a collisionless plasma, Math. Meth. Appl. Sci. (2011), to appear. |
[9] |
B. Perthame, Time decay, propagation of low moments and dispersive effects for kinetic equations, Comm. P.D.E., 21 (1996), 659-686. |
[10] |
K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Eqns., 95 (1992), 281-303.
doi: 10.1016/0022-0396(92)90033-J. |
[11] |
G. Rein, Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case, Math. Nachr., 191 (1998), 269-278.
doi: 10.1002/mana.19981910114. |
[12] |
G. Rein, Collisionless kinetic equations from astrophysics -- the Vlasov-Poisson system, Handbook of differential equations: evolutionary equations, Vol. III, 383-476, Elsevier/North-Holland, Amsterdam, 2007. |
[13] |
D. Salort, Transport equations with unbounded force fields and application to the Vlasov-Poisson equation, Math. Models Methods Appl. Sci., 19 (2009), 199-228.
doi: 10.1142/S0218202509003401. |
[14] |
J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. P.D.E., 16 (1991), 1313-1335.
doi: 10.1080/03605309108820801. |
[15] |
J. Schaeffer, Asymptotic growth bounds for the Vlasov-Poisson system, Math. Meth. Appl. Sci., 34 (2010), 262-277.
doi: 10.1002/mma.1354. |
show all references
References:
[1] |
C. Bardos and P. Degond, Global existence for the Vlasov Poisson equation in $3$ space variables with small initial data, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2 (1985), 101-118. |
[2] |
J. Batt, M. Kunze and G. Rein, On the asymptotic behaviour of a one-dimensional monocharged plasma, Adv. Differential Equations, 3 (1998), 271-292. |
[3] |
R. Glassey, "The Cauchy Problem in Kinetic Theory," SIAM, 1996. |
[4] |
E. Horst, Symmetric plasmas and their decay, Comm. Math. Phys., 126 (1990), 613-633.
doi: 10.1007/BF02125703. |
[5] |
E. Horst, On the asymptotic growth of the solutions of the Vlasov-Poisson system, Math. Meth. Appl. Sci., 16 (1993), 75-85.
doi: 10.1002/mma.1670160202. |
[6] |
R. Illner and G. Rein, Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case, Math. Meth. Appl. Sci., 19 (1996), 1409-1413.
doi: 10.1002/(SICI)1099-1476(19961125)19:17<1409::AID-MMA836>3.0.CO;2-2. |
[7] |
P. L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., 105 (1991), 415-430.
doi: 10.1007/BF01232273. |
[8] |
C. Pallard, A note on the growth of velocities in a collisionless plasma, Math. Meth. Appl. Sci. (2011), to appear. |
[9] |
B. Perthame, Time decay, propagation of low moments and dispersive effects for kinetic equations, Comm. P.D.E., 21 (1996), 659-686. |
[10] |
K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Eqns., 95 (1992), 281-303.
doi: 10.1016/0022-0396(92)90033-J. |
[11] |
G. Rein, Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case, Math. Nachr., 191 (1998), 269-278.
doi: 10.1002/mana.19981910114. |
[12] |
G. Rein, Collisionless kinetic equations from astrophysics -- the Vlasov-Poisson system, Handbook of differential equations: evolutionary equations, Vol. III, 383-476, Elsevier/North-Holland, Amsterdam, 2007. |
[13] |
D. Salort, Transport equations with unbounded force fields and application to the Vlasov-Poisson equation, Math. Models Methods Appl. Sci., 19 (2009), 199-228.
doi: 10.1142/S0218202509003401. |
[14] |
J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. P.D.E., 16 (1991), 1313-1335.
doi: 10.1080/03605309108820801. |
[15] |
J. Schaeffer, Asymptotic growth bounds for the Vlasov-Poisson system, Math. Meth. Appl. Sci., 34 (2010), 262-277.
doi: 10.1002/mma.1354. |
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