DG - MP - PDE Seminar: Reinel Sospedra Alfonso (UBC)
Topic
Uniqueness of the compactly supported wweak solutions of the relativistic Vlasov-Darwin system
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Abstract
The relativistic Vlasov-Darwin (RVD) system is a kinetic model that describes the evolution of a collisionless plasma whose particles interact through the self-induced electromagnetic field. In contrast with the Vlasov-Maxwell system, the particle interaction is assumed to be a low-order relativistic correction (i.e., the Darwin approximation) to the full Maxwell case. A consequence of this assumption is that instead of the less tractable hyperbolic Maxwell equations, the resulting system has elliptic features even though there is a fully coupled magnetic field. We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the RVD system. Our proof extends the method used by Loeper in [J. Math. Pures Appl., 86 (2006), pp. 68-79 ] to obtain uniqueness results for the Vlasov-Poisson system. This is a joint work with Martial Agueh.
The relativistic Vlasov-Darwin (RVD) system is a kinetic model that describes the evolution of a collisionless plasma whose particles interact through the self-induced electromagnetic field. In contrast with the Vlasov-Maxwell system, the particle interaction is assumed to be a low-order relativistic correction (i.e., the Darwin approximation) to the full Maxwell case. A consequence of this assumption is that instead of the less tractable hyperbolic Maxwell equations, the resulting system has elliptic features even though there is a fully coupled magnetic field. We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the RVD system. Our proof extends the method used by Loeper in [J. Math. Pures Appl., 86 (2006), pp. 68-79 ] to obtain uniqueness results for the Vlasov-Poisson system. This is a joint work with Martial Agueh.
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Reinel Sospedra Alfonso (UBC)
Reinel Sospedra Alfonso (UBC)