Goursat problem for the Yang-Mills-Vlasov system in temporal gauge
This article studies the characteristic Cauchy problem for the Yang-Mills-Vlasov (YMV) system in temporal gauge, where the initial data are specified on two intersecting smooth characteristic hypersurfaces of Minkowski spacetime $(mathbb{R}^{4},eta )$. Under a $mathcal{C}^{infty }$ hypothesis o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2011-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2011/163/abstr.html |
| _version_ | 1818564424678506496 |
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| author | Marcel Dossa Marcel Nanga |
| author_facet | Marcel Dossa Marcel Nanga |
| author_sort | Marcel Dossa |
| collection | DOAJ |
| description | This article studies the characteristic Cauchy problem for the Yang-Mills-Vlasov (YMV) system in temporal gauge, where the initial data are specified on two intersecting smooth characteristic hypersurfaces of Minkowski spacetime $(mathbb{R}^{4},eta )$. Under a $mathcal{C}^{infty }$ hypothesis on the data, we solve the initial constraint problem and the evolution problem. Local in time existence and uniqueness results are established thanks to a suitable combination of the method of characteristics, Leray's Theory of hyperbolic systems and techniques developed by Choquet-Bruhat for ordinary spatial Cauchy problems related to (YMV) systems. |
| first_indexed | 2024-12-14T01:28:44Z |
| format | Article |
| id | doaj.art-60c9961cac124b61bb3f45dd91c94f52 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T01:28:44Z |
| publishDate | 2011-12-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-60c9961cac124b61bb3f45dd91c94f522022-12-21T23:22:06ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-12-012011163,122Goursat problem for the Yang-Mills-Vlasov system in temporal gaugeMarcel DossaMarcel NangaThis article studies the characteristic Cauchy problem for the Yang-Mills-Vlasov (YMV) system in temporal gauge, where the initial data are specified on two intersecting smooth characteristic hypersurfaces of Minkowski spacetime $(mathbb{R}^{4},eta )$. Under a $mathcal{C}^{infty }$ hypothesis on the data, we solve the initial constraint problem and the evolution problem. Local in time existence and uniqueness results are established thanks to a suitable combination of the method of characteristics, Leray's Theory of hyperbolic systems and techniques developed by Choquet-Bruhat for ordinary spatial Cauchy problems related to (YMV) systems.http://ejde.math.txstate.edu/Volumes/2011/163/abstr.htmlGoursat problemcharacteristic initial hypersurfacesYang-Mills-Vlasov systemtemporal gaugeinitialconstraintsevolution problem |
| spellingShingle | Marcel Dossa Marcel Nanga Goursat problem for the Yang-Mills-Vlasov system in temporal gauge Electronic Journal of Differential Equations Goursat problem characteristic initial hypersurfaces Yang-Mills-Vlasov system temporal gauge initial constraints evolution problem |
| title | Goursat problem for the Yang-Mills-Vlasov system in temporal gauge |
| title_full | Goursat problem for the Yang-Mills-Vlasov system in temporal gauge |
| title_fullStr | Goursat problem for the Yang-Mills-Vlasov system in temporal gauge |
| title_full_unstemmed | Goursat problem for the Yang-Mills-Vlasov system in temporal gauge |
| title_short | Goursat problem for the Yang-Mills-Vlasov system in temporal gauge |
| title_sort | goursat problem for the yang mills vlasov system in temporal gauge |
| topic | Goursat problem characteristic initial hypersurfaces Yang-Mills-Vlasov system temporal gauge initial constraints evolution problem |
| url | http://ejde.math.txstate.edu/Volumes/2011/163/abstr.html |
| work_keys_str_mv | AT marceldossa goursatproblemfortheyangmillsvlasovsystemintemporalgauge AT marcelnanga goursatproblemfortheyangmillsvlasovsystemintemporalgauge |