DG - MP - PDE Seminar: Reinel Sospedra Alfonso (UBC)

  • Date: 10/18/2011
  • Time: 15:30
Reinel Sospedra Alfonso (UBC)

University of British Columbia


Uniqueness of the compactly supported wweak solutions of the relativistic Vlasov-Darwin system


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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