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 |
| Summary: | 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. |
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| ISSN: | 1072-6691 |