Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system
Reinel Sospedra-Alfonso, Martial Agueh
TL;DR
This paper proves the uniqueness of compactly supported weak solutions for the relativistic Vlasov-Darwin system using optimal transportation methods, extending previous techniques from the Vlasov-Poisson system.
Contribution
It introduces a novel application of optimal transportation to establish uniqueness in the relativistic Vlasov-Darwin system, expanding the scope of existing mathematical methods.
Findings
Proves uniqueness of weak solutions for the system.
Extends Loeper's method to a relativistic context.
Uses optimal transportation techniques.
Abstract
We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in J. Math. Pures Appl. 86, 68-79 (2006) to obtain uniqueness results for the Vlasov-Poisson system.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGas Dynamics and Kinetic Theory · Navier-Stokes equation solutions · Geometric Analysis and Curvature Flows