On the Evolution Problem for the Einstein-Vlasov System

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• 作者：Calvin Tadmon
• 关键词：Einstein ; Vlasov system ; Gravitational field ; Distribution function ; Evolution problem ; Sobolev inequalities ; Moser estimates
• 刊名：Acta Mathematica Vietnamica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：42
• 期：1
• 页码：163-186
• 全文大小：
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2315-4144
• 卷排序：42

文摘

In this work, we solve the evolution problem associated with the Einstein-Vlasov system, with initial data specified on two transversally intersecting null hypersurfaces. The main existence and uniqueness result of the paper is obtained by a contracting mapping principle, combined with Sobolev inequalities and Moser estimates as well as energy inequalities for first order and second order linear hyperbolic systems. The whole investigation is conducted in appropriate weighted Sobolev spaces.