Skip to main content
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
/content/aip/journal/jmp/57/8/10.1063/1.4960743
1.
Bardos, C. and Degond, P. , “Global existence for the Vlasov-Poisson equation in 3-space variables with small initial data,” Ann. Inst. Henri Poincare Anal. Non Linéaire 2, 101-118 (1985).
2.
Batt, J. , “Global symmetric solutions of the initial value problem of stellar dynamics,” J. Differ. Equations 25, 342-364 (1977).
http://dx.doi.org/10.1016/0022-0396(77)90049-3
3.
Bauer, S. and Kunze, M. , “The Darwin approximation of the relativistic Vlasov-Maxwell system,” Ann. Henri Poincaré 6, 283-308 (2005).
http://dx.doi.org/10.1007/s00023-005-0207-y
4.
Benachour, S. , Filbet, F. , Laurencot, P. , and Sonnendrücker, E. , “Global existence for the Vlasov-Darwin system in R3 for small initial data,” Math. Methods Appl. Sci. 26, 297-319 (2003).
http://dx.doi.org/10.1002/mma.355
5.
Degond, P. and Raviart, P. A. , “An analysis of the Darwin model of approximation to Maxwell’s equation,” Forum Math. 4, 13-44 (1992).
http://dx.doi.org/10.1515/form.1992.4.13
6.
Gilbarg, D. and Trudinger, N. S. , Elliptic Partial Differential Equations of Second Order (Springer, Berlin, 2001).
7.
Glassey, R. T. and Schaeffer, J. , “On symmetric solutions of the relativistic Vlasov-Poisson system,” Commun. Math. Phys. 101, 459-473 (1985).
http://dx.doi.org/10.1007/BF01210740
8.
Glassey, R. T. and Strauss, W. A. , “Singularity formation in a collisionless plasma could occur only at high velocities,” Arch. Ration. Mech. Anal. 92, 59-90 (1986).
http://dx.doi.org/10.1007/BF00250732
9.
Glassey, R. T. and Strauss, W. A. , “Absence of shocks in an initially dilute collisionless plasma,” Commun. Math. Phys. 113, 191-208 (1987).
http://dx.doi.org/10.1007/BF01223511
10.
Glassey, R. T. and Schaeffer, J. , “Global existence for the relativistic Vlasov-Maxwell system with nearly neutral initial data,” Commun. Math. Phys. 119, 353-384 (1988).
http://dx.doi.org/10.1007/BF01218078
11.
Glassey, R. T. and Schaeffer, J. , “On the ‘one and one-half dimensional’ relativistic Vlasov-Maxwell system,” Math. Methods Appl. Sci. 13, 169-179 (1990).
http://dx.doi.org/10.1002/mma.1670130207
12.
Glassey, R. T. , The Cauchy Problem in Kinetic Theory (Society of Indian Automobile Manufactures, Philadelphia, 1996).
13.
Glassey, R. T. and Schaeffer, J. , “The ‘two and one-half dimensional’ relativistic Vlasov-Maxwell system,” Commun. Math. Phys. 185, 257-284 (1997).
http://dx.doi.org/10.1007/s002200050090
14.
Glassey, R. T. and Schaeffer, J. , “The relativistic Vlasov-Maxwell system in two space dimensions: Part I,” Arch. Ration. Mech. Anal. 141, 331-354 (1998).
http://dx.doi.org/10.1007/s002050050079
15.
Glassey, R. T. and Schaeffer, J. , “The relativistic Vlasov-Maxwell system in two space dimensions: Part II,” Arch. Ration. Mech. Anal. 141, 355-374 (1998).
http://dx.doi.org/10.1007/s002050050080
16.
Glassey, R. T. and Schaeffer, J. , “On global symmetric solutions of the relativistic Vlasov-Poisson equation in three space dimensions,” Math. Methods Appl. Sci. 24, 143-157 (2001).
http://dx.doi.org/10.1002/1099-1476(200102)24:3<143::AID-MMA202>3.0.CO;2-C
17.
Hartman, P. , Ordinary Differential Equations (Wiley, New York, 1964).
18.
Horst, E. , “On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation. I. General theory,” Math. Methods Appl. Sci. 3, 229-248 (1981).
http://dx.doi.org/10.1002/mma.1670030117
19.
Horst, E. , “On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation. II. Special cases,” Math. Methods Appl. Sci. 4, 19-32 (1982).
http://dx.doi.org/10.1002/mma.1670040104
20.
Horst, E. , “Symmetric plasmas and their decay,” Commun. Math. Phys. 126, 613-633 (1990).
http://dx.doi.org/10.1007/BF02125703
21.
Horst, E. and Hunze, R. , “Weak solutions of the initial value problem for the unmodified non-linear Vlasov equation,” Math. Methods Appl. Sci. 6, 262-279 (1984).
http://dx.doi.org/10.1002/mma.1670060118
22.
Lieb, E. and Loss, M. , “Analysis,” in Graduate Studies in Mathematics (American Mathematical Society, Providence, 1997), Vol. 14.
23.
Lions, P.-L. and Perthame, B. , “Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system,” Invent. Math. 105, 415-430 (1991).
http://dx.doi.org/10.1007/BF01232273
24.
Loeper, G. , “Uniqueness of the solution to Vlasov-Poisson system with bounded density,” J. Math. Pures Appl. 86, 68-79 (2006).
http://dx.doi.org/10.1016/j.matpur.2006.01.005
25.
Pallard, C. , “The initial value problem for the relativistic Vlasov-Darwin system,” Int. Math. Res. Not. 2006, 1-31.
http://dx.doi.org/10.1155/imrn/2006/57191
26.
Pfaffelmoser, K. , “Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data,” J. Differ. Equations 95, 281-303 (1992).
http://dx.doi.org/10.1016/0022-0396(92)90033-J
27.
Rein, G. , “Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics,” Commun. Math. Phys. 135, 41-78 (1990).
http://dx.doi.org/10.1007/BF02097656
28.
Rein, G. , “Collisionless kinetic equation from astrophysics-the Vlasov-Poisson system,” in Handbook of Differential Equations: Evolutionary Equations (Elsevier, 2007), Vol. 3, pp. 383-476.
29.
Schaeffer, J. , “Global existence for the Poisson-Vlasov system with nealy symmetric data,” J. Differ. Equations 69, 111-148 (1987).
http://dx.doi.org/10.1016/0022-0396(87)90105-7
30.
Seehafer, M. , “Global classical solutions of the Vlasov-Darwin system for small initial data,” Commun. Math. Sci. 6, 749-764 (2008).
http://dx.doi.org/10.4310/CMS.2008.v6.n3.a11
31.
Sospedra-Alfonso, R. and Agueh, M. , “Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system,” Acta Appl. Math. 124, 207-227 (2013).
http://dx.doi.org/10.1007/s10440-012-9776-1
32.
Sospedra-Alfonso, R. , Agueh, M. , and Illner, R. , “Global classical solutions of the relativistic Vlasov-Darwin system with small Cauchy data: The generalized variables approach,” Arch. Ration. Mech. Anal. 205, 827-869 (2012).
http://dx.doi.org/10.1007/s00205-012-0518-3
33.
Wollman, S. , “An existence and uniquness theorem for the Vlasov-Maxwell system,” Commun. Pure Appl. Math. 37, 457-462 (1984).
http://dx.doi.org/10.1002/cpa.3160370404
http://aip.metastore.ingenta.com/content/aip/journal/jmp/57/8/10.1063/1.4960743
Loading
/content/aip/journal/jmp/57/8/10.1063/1.4960743
Loading

Data & Media loading...

Loading

Article metrics loading...

/content/aip/journal/jmp/57/8/10.1063/1.4960743
2016-08-15
2016-09-26

Abstract

We study the Cauchy problem of the relativistic Vlasov-Darwin system with generalized variables proposed by Sospedra-Alfonso [“Global classical solutions of the relativistic Vlasov-Darwin system with small Cauchy data: the generalized variables approach,” Arch. Ration. Mech. Anal. , 827-869 (2012)]. We prove global existence of a non-negative classical solution to the Cauchy problem in three space variables under small perturbation of the initial datum, and as a consequence, we obtain that nearly spherically symmetric solutions with required regularity exist globally in time.

Loading

Full text loading...

/deliver/fulltext/aip/journal/jmp/57/8/1.4960743.html;jsessionid=Lp2rm1bBXSlj6vLtWxQwiEqU.x-aip-live-03?itemId=/content/aip/journal/jmp/57/8/10.1063/1.4960743&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/jmp
true
true

Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
/content/realmedia?fmt=ahah&adPositionList=
&advertTargetUrl=//oascentral.aip.org/RealMedia/ads/&sitePageValue=jmp.aip.org/57/8/10.1063/1.4960743&pageURL=http://scitation.aip.org/content/aip/journal/jmp/57/8/10.1063/1.4960743'
Right1,Right2,Right3,