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A Vlasov-Poisson plasma with unbounded mass and velocities confined in a cylinder by a magnetic mirror
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 |
References:
[1] |
E. Caglioti, S. Caprino, C. Marchioro and M. Pulvirenti, The Vlasov equation with infinite mass, Arch. Rat. Mech. Anal., 159 (2001), 85-108.
doi: 10.1007/s002050100150. |
[2] |
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.
doi: 10.1081/PDE-120002874. |
[3] |
S. Caprino, G. Cavallaro and C. Marchioro, Time evolution of a Vlasov-Poisson plasma with magnetic confinement, Kinetic and Related Models, 5 (2012), 729-742.
doi: 10.3934/krm.2012.5.729. |
[4] |
S. Caprino, G. Cavallaro and C. Marchioro, On a magnetically confined plasma with infinite charge, SIAM J. Math. Anal., 46 (2014), 133-164.
doi: 10.1137/130916527. |
[5] |
S. Caprino, G. Cavallaro and C. Marchioro, Remark on a magnetically confined plasma with infinite charge, Rend. Mat. Appl., 35 (2014), 69-98. |
[6] |
S. Caprino, G. Cavallaro and C. Marchioro, On a Vlasov-Poisson plasma confined in a torus by a magnetic mirror, J. Math. Anal. Appl., 427 (2015), 31-46.
doi: 10.1016/j.jmaa.2015.02.012. |
[7] |
R. Glassey, The Cauchy Problem in Kinetic Theory, SIAM, Philadelphia, PA, 1996.
doi: 10.1137/1.9781611971477. |
[8] |
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. |
[9] |
T. Nguyen, V. Nguyen and W. Strauss, Global magnetic confinement for the 1.5D Vlasov-Maxwell system, Kinetic and Related Models, 8 (2015), 153-168.
doi: 10.3934/krm.2015.8.153. |
[10] |
S. Pankavich, Global existence for the three dimensional Vlasov-Poisson system with steady spatial asymptotics, Comm. Part. Diff. Eq., 31 (2006), 349-370.
doi: 10.1080/03605300500358004. |
[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.
doi: 10.1016/0022-0396(92)90033-J. |
[12] |
J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. Part. Diff. Eq., 16 (1991), 1313-1335.
doi: 10.1080/03605309108820801. |
[13] |
J. Schaeffer, The Vlasov-Poisson system with steady spatial asymptotics, Comm. Part. Diff. Eq., 28 (2003), 1057-1084.
doi: 10.1081/PDE-120021186. |
[14] |
J. Schaeffer, Steady spatial asymptotics for the Vlasov-Poisson system, Math. Meth. Appl. Sci., 26 (2003), 273-296.
doi: 10.1002/mma.354. |
[15] |
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. |
[16] |
S. Wollman, Global in time solution to the three-dimensional Vlasov-Poisson system, J. Math. Anal. Appl., 176 (1993), 76-91.
doi: 10.1006/jmaa.1993.1200. |
show all references
References:
[1] |
E. Caglioti, S. Caprino, C. Marchioro and M. Pulvirenti, The Vlasov equation with infinite mass, Arch. Rat. Mech. Anal., 159 (2001), 85-108.
doi: 10.1007/s002050100150. |
[2] |
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.
doi: 10.1081/PDE-120002874. |
[3] |
S. Caprino, G. Cavallaro and C. Marchioro, Time evolution of a Vlasov-Poisson plasma with magnetic confinement, Kinetic and Related Models, 5 (2012), 729-742.
doi: 10.3934/krm.2012.5.729. |
[4] |
S. Caprino, G. Cavallaro and C. Marchioro, On a magnetically confined plasma with infinite charge, SIAM J. Math. Anal., 46 (2014), 133-164.
doi: 10.1137/130916527. |
[5] |
S. Caprino, G. Cavallaro and C. Marchioro, Remark on a magnetically confined plasma with infinite charge, Rend. Mat. Appl., 35 (2014), 69-98. |
[6] |
S. Caprino, G. Cavallaro and C. Marchioro, On a Vlasov-Poisson plasma confined in a torus by a magnetic mirror, J. Math. Anal. Appl., 427 (2015), 31-46.
doi: 10.1016/j.jmaa.2015.02.012. |
[7] |
R. Glassey, The Cauchy Problem in Kinetic Theory, SIAM, Philadelphia, PA, 1996.
doi: 10.1137/1.9781611971477. |
[8] |
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. |
[9] |
T. Nguyen, V. Nguyen and W. Strauss, Global magnetic confinement for the 1.5D Vlasov-Maxwell system, Kinetic and Related Models, 8 (2015), 153-168.
doi: 10.3934/krm.2015.8.153. |
[10] |
S. Pankavich, Global existence for the three dimensional Vlasov-Poisson system with steady spatial asymptotics, Comm. Part. Diff. Eq., 31 (2006), 349-370.
doi: 10.1080/03605300500358004. |
[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.
doi: 10.1016/0022-0396(92)90033-J. |
[12] |
J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Comm. Part. Diff. Eq., 16 (1991), 1313-1335.
doi: 10.1080/03605309108820801. |
[13] |
J. Schaeffer, The Vlasov-Poisson system with steady spatial asymptotics, Comm. Part. Diff. Eq., 28 (2003), 1057-1084.
doi: 10.1081/PDE-120021186. |
[14] |
J. Schaeffer, Steady spatial asymptotics for the Vlasov-Poisson system, Math. Meth. Appl. Sci., 26 (2003), 273-296.
doi: 10.1002/mma.354. |
[15] |
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. |
[16] |
S. Wollman, Global in time solution to the three-dimensional Vlasov-Poisson system, J. Math. Anal. Appl., 176 (1993), 76-91.
doi: 10.1006/jmaa.1993.1200. |
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