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Global classical solutions close to equilibrium to the Vlasov-Fokker-Planck-Euler system
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On a charge interacting with a plasma of unbounded mass
1. | Dipartimento di Matematica, Università di Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma |
2. | Dipartimento di Matematica, Università La Sapienza, Piazzale Aldo Moro 2, 00185 Roma |
References:
[1] |
P. Butta', G. Ferrari and C. Marchioro, Speedy motions of a body immersed in an infinitely extended medium,, Jour. Stat. Phys., 140 (2010), 1182. Google Scholar |
[2] |
E. Caglioti, S. Caprino, C. Marchioro and M. Pulvirenti, The Vlasov equation with infinite mass,, Arch. Rational Mech. Anal., 159 (2001), 85.
doi: 10.1007/s002050100150. |
[3] |
S. Caprino and C. Marchioro, On the plasma-charge model,, Kinetic and Related Problems, 3 (2010), 241. Google Scholar |
[4] |
S. Caprino, C. Marchioro and M. Pulvirenti, On the two dimensional Vlasov-Helmholtz equation with infinite mass,, Commun. PDE, 27 (2002), 791.
doi: 10.1081/PDE-120002874. |
[5] |
E. Horst, On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation I,, Math. Meth. Appl. Sci., 3 (1981), 229.
doi: 10.1002/mma.1670030117. |
[6] |
E. Horst, On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation II,, Math. Meth. Appl. Sci., 4 (1982), 19.
doi: 10.1002/mma.1670040104. |
[7] |
P. L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system,, Invent. Math., 105 (1996), 415.
doi: 10.1007/BF01232273. |
[8] |
G. Loeper, Uniqueness of the solution to the Vlasov-Poisson system with bounded density,, Jour. de Math. Pure Appl., 86 (2006), 68.
|
[9] |
A. Majda, G. Majda and Y. Zheng, Concentrations in the one-dimensional Vlasov-Poisson equations. I. Temporal development and non-unique weak solutions in the single component case,, Phys. D, 74 (1994), 268.
doi: 10.1016/0167-2789(94)90198-8. |
[10] |
A. Majda, G. Majda and Y. Zheng, Concentrations in the one-dimensional Vlasov-Poisson equations. II. Screening and the necessity for measure-valued solutions in the two component case,, Phys. D, 79 (1994), 41.
doi: 10.1016/0167-2789(94)90037-X. |
[11] |
C. Marchioro, E. Miot and M. Pulvirenti, The Cauchy problem for the 3-D Vlasov-Poisson system with point charges,, Arch. Rational Mech. Anal. (2010) in press., (2010). Google Scholar |
[12] |
S. Okabe and T. Ukai, On classical solutions in the large in time for the two-dimensional Vlasov's equation,, Osaka Jour. Math., 15 (1978), 245.
|
[13] |
S. Pankavich, Global existence for the three dimensional Vlasov-Poisson system with steady spatial asymptotics,, Comm. PDE, 31 (2006), 349.
doi: 10.1080/03605300500358004. |
[14] |
K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data,, Jour. Diff. Eq., 95 (1992), 281.
doi: 10.1016/0022-0396(92)90033-J. |
[15] |
D. Salort, Transport equations with unbounded force fields and application to the Vlasov-Poisson equation,, Math. Mod. Meth. Appl. Sci., 19 (2009), 199.
doi: 10.1142/S0218202509003401. |
[16] |
J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions,, Commun. PDE., 16 (1991), 1313.
|
[17] |
S. Wollman, Global in time solutions to the two-dimensional Vlasov-Poisson system,, Commun. Pure Appl. Math., 33 (1980), 173.
doi: 10.1002/cpa.3160330205. |
[18] |
S. Wollman, Global in time solution to the three-dimensional Vlasov-Poisson system,, Jour. Math. Anal. Appl., 176 (1993), 76.
doi: 10.1006/jmaa.1993.1200. |
[19] |
Y. Zheng and A. Majda, Existence of global weak solutions to one-component Vlasov-Poisson and Fokker-Planck-Poisson systems in one space dimension with measures as initial data,, Comm. Pure Appl. Math., 47 (1994), 1365.
doi: 10.1002/cpa.3160471004. |
show all references
References:
[1] |
P. Butta', G. Ferrari and C. Marchioro, Speedy motions of a body immersed in an infinitely extended medium,, Jour. Stat. Phys., 140 (2010), 1182. Google Scholar |
[2] |
E. Caglioti, S. Caprino, C. Marchioro and M. Pulvirenti, The Vlasov equation with infinite mass,, Arch. Rational Mech. Anal., 159 (2001), 85.
doi: 10.1007/s002050100150. |
[3] |
S. Caprino and C. Marchioro, On the plasma-charge model,, Kinetic and Related Problems, 3 (2010), 241. Google Scholar |
[4] |
S. Caprino, C. Marchioro and M. Pulvirenti, On the two dimensional Vlasov-Helmholtz equation with infinite mass,, Commun. PDE, 27 (2002), 791.
doi: 10.1081/PDE-120002874. |
[5] |
E. Horst, On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation I,, Math. Meth. Appl. Sci., 3 (1981), 229.
doi: 10.1002/mma.1670030117. |
[6] |
E. Horst, On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation II,, Math. Meth. Appl. Sci., 4 (1982), 19.
doi: 10.1002/mma.1670040104. |
[7] |
P. L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system,, Invent. Math., 105 (1996), 415.
doi: 10.1007/BF01232273. |
[8] |
G. Loeper, Uniqueness of the solution to the Vlasov-Poisson system with bounded density,, Jour. de Math. Pure Appl., 86 (2006), 68.
|
[9] |
A. Majda, G. Majda and Y. Zheng, Concentrations in the one-dimensional Vlasov-Poisson equations. I. Temporal development and non-unique weak solutions in the single component case,, Phys. D, 74 (1994), 268.
doi: 10.1016/0167-2789(94)90198-8. |
[10] |
A. Majda, G. Majda and Y. Zheng, Concentrations in the one-dimensional Vlasov-Poisson equations. II. Screening and the necessity for measure-valued solutions in the two component case,, Phys. D, 79 (1994), 41.
doi: 10.1016/0167-2789(94)90037-X. |
[11] |
C. Marchioro, E. Miot and M. Pulvirenti, The Cauchy problem for the 3-D Vlasov-Poisson system with point charges,, Arch. Rational Mech. Anal. (2010) in press., (2010). Google Scholar |
[12] |
S. Okabe and T. Ukai, On classical solutions in the large in time for the two-dimensional Vlasov's equation,, Osaka Jour. Math., 15 (1978), 245.
|
[13] |
S. Pankavich, Global existence for the three dimensional Vlasov-Poisson system with steady spatial asymptotics,, Comm. PDE, 31 (2006), 349.
doi: 10.1080/03605300500358004. |
[14] |
K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data,, Jour. Diff. Eq., 95 (1992), 281.
doi: 10.1016/0022-0396(92)90033-J. |
[15] |
D. Salort, Transport equations with unbounded force fields and application to the Vlasov-Poisson equation,, Math. Mod. Meth. Appl. Sci., 19 (2009), 199.
doi: 10.1142/S0218202509003401. |
[16] |
J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions,, Commun. PDE., 16 (1991), 1313.
|
[17] |
S. Wollman, Global in time solutions to the two-dimensional Vlasov-Poisson system,, Commun. Pure Appl. Math., 33 (1980), 173.
doi: 10.1002/cpa.3160330205. |
[18] |
S. Wollman, Global in time solution to the three-dimensional Vlasov-Poisson system,, Jour. Math. Anal. Appl., 176 (1993), 76.
doi: 10.1006/jmaa.1993.1200. |
[19] |
Y. Zheng and A. Majda, Existence of global weak solutions to one-component Vlasov-Poisson and Fokker-Planck-Poisson systems in one space dimension with measures as initial data,, Comm. Pure Appl. Math., 47 (1994), 1365.
doi: 10.1002/cpa.3160471004. |
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