The non-relativistic limit of the Nordström-Vlasov system

Details The non-relativistic limit of the Nordström-Vlasov system The non-relativistic limit of the Nordström-Vlasov system

2003-09-12

arxiv.org/abs/math-ph/0309030v2

Comm. Math. Sci. 2 (2004) 19-34

Physics

Mathematical Physics

19 pages

Scientific paper

The Nordstr\"om-Vlasov system provides an interesting relativistic generalization of the Vlasov-Poisson system in the gravitational case, even though there is no direct physical application. The study of this model will probably lead to a better mathematical understanding of the class of non-linear systems consisting of hyperbolic and transport equations. In this paper it is shown that solutions of the Nordstr\"om-Vlasov system converge to solutions of the Vlasov-Poisson system in a pointwise sense as the speed of light tends to infinity, providing a further and rigorous justification of this model as a \textit{genuine} relativistic generalization of the Vlasov-Poisson system.

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