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Time evolution of a Vlasov-Poisson plasma with magnetic confinement
1. | Dipartimento di Matematica, Università di Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma |
2. | Dipartimento di Matematica "Guido Castelnuovo", Università La Sapienza P.le A. Moro 5, 00185 Roma, Italy, Italy |
References:
[1] |
J. Batt and G. Rein, Global classical solutions of a periodic Vlasov-Poisson system in three dimensions, C. R. Acad. Sci. Paris, 313 S. I. (1991), 411-416. |
[2] |
S. Caprino and C. Marchioro, On the plasma-charge model, Kinetic and Related Models, 3 (2010), 241-254. |
[3] |
S. Caprino and C. Marchioro, On a charge interacting with a plasma of unbounded mass, Kinetic and Related Models, 4 (2011), 215-226. |
[4] |
S. Caprino, C. Marchioro and M. Pulvirenti, On the two dimensional Vlasov-Helmholtz equation with infinite mass, Comm. Part. Diff. Eq., 27 (2002), 791-808. |
[5] |
S. Caprino, C. Marchioro, E. Miot and M. Pulvirenti, On the attractive plasma-charge system in 2-d, Comm. Part. Diff. Eq., 37 (2012), 1237-1272.
doi: 10.1080/3605302.2011.653032. |
[6] |
R. Glassey, "The Cauchy Problem in Kinetic Theory," SIAM: Philadelphia, PA, 1996. |
[7] |
P. E. Jabin, The Vlasov-Poisson system with infinite mass and energy, J. Stat. Phys., 103 (2001), 1107-1123. |
[8] |
P. L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., 105 (1996), 415-430. |
[9] |
C. Marchioro, E. Miot and M. Pulvirenti, The Cauchy problem for the 3-D Vlasov-Poisson system with point charges, Arch. Rat. Mech. Anal., 201 (2011), 1-26.
doi: 10.1007/s00205-010-0388-5. |
[10] |
S. Pankavich, Global existence for the three dimensional Vlasov-Poisson system with steady spatial asymptotics, Comm. Part. Diff. Eq., 31 (2006), 349-370. |
[11] |
K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, Jour. Diff. Eq., 95 (1992), 281-303. |
[12] |
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. |
[13] |
D. Salort, Transport equations with unbounded force fields and application to the Vlasov-Poisson equation, Math. Mod. Meth. Appl. Sci., 19 (2009), 199-228. |
[14] |
J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. Part. Diff. Eq., 16 (1991), 1313-1335. |
[15] |
J. Schaeffer, The Vlasov-Poisson system with steady spatial asymptotics, Comm. Part. Diff. Eq., 28 (2003), 1057-1084. |
[16] |
J. Schaeffer, Global existence for the Vlasov-Poisson system with steady spatial asymptotic behavior, Kinetic and Related Models, 5 (2012), 129-153.
doi: 10.3934/krm.2012.5.129. |
[17] |
S. Wollman, Global in time solution to the three-dimensional Vlasov-Poisson system, Jour. Math. Anal. Appl., 176 (1993), 76-91. |
show all references
References:
[1] |
J. Batt and G. Rein, Global classical solutions of a periodic Vlasov-Poisson system in three dimensions, C. R. Acad. Sci. Paris, 313 S. I. (1991), 411-416. |
[2] |
S. Caprino and C. Marchioro, On the plasma-charge model, Kinetic and Related Models, 3 (2010), 241-254. |
[3] |
S. Caprino and C. Marchioro, On a charge interacting with a plasma of unbounded mass, Kinetic and Related Models, 4 (2011), 215-226. |
[4] |
S. Caprino, C. Marchioro and M. Pulvirenti, On the two dimensional Vlasov-Helmholtz equation with infinite mass, Comm. Part. Diff. Eq., 27 (2002), 791-808. |
[5] |
S. Caprino, C. Marchioro, E. Miot and M. Pulvirenti, On the attractive plasma-charge system in 2-d, Comm. Part. Diff. Eq., 37 (2012), 1237-1272.
doi: 10.1080/3605302.2011.653032. |
[6] |
R. Glassey, "The Cauchy Problem in Kinetic Theory," SIAM: Philadelphia, PA, 1996. |
[7] |
P. E. Jabin, The Vlasov-Poisson system with infinite mass and energy, J. Stat. Phys., 103 (2001), 1107-1123. |
[8] |
P. L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. Math., 105 (1996), 415-430. |
[9] |
C. Marchioro, E. Miot and M. Pulvirenti, The Cauchy problem for the 3-D Vlasov-Poisson system with point charges, Arch. Rat. Mech. Anal., 201 (2011), 1-26.
doi: 10.1007/s00205-010-0388-5. |
[10] |
S. Pankavich, Global existence for the three dimensional Vlasov-Poisson system with steady spatial asymptotics, Comm. Part. Diff. Eq., 31 (2006), 349-370. |
[11] |
K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, Jour. Diff. Eq., 95 (1992), 281-303. |
[12] |
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. |
[13] |
D. Salort, Transport equations with unbounded force fields and application to the Vlasov-Poisson equation, Math. Mod. Meth. Appl. Sci., 19 (2009), 199-228. |
[14] |
J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. Part. Diff. Eq., 16 (1991), 1313-1335. |
[15] |
J. Schaeffer, The Vlasov-Poisson system with steady spatial asymptotics, Comm. Part. Diff. Eq., 28 (2003), 1057-1084. |
[16] |
J. Schaeffer, Global existence for the Vlasov-Poisson system with steady spatial asymptotic behavior, Kinetic and Related Models, 5 (2012), 129-153.
doi: 10.3934/krm.2012.5.129. |
[17] |
S. Wollman, Global in time solution to the three-dimensional Vlasov-Poisson system, Jour. Math. Anal. Appl., 176 (1993), 76-91. |
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