A New Continuation Criterion for the Relativistic Vlasov–Maxwell System
A New Continuation Criterion for the Relativistic Vlasov–Maxwell System
复制标题
相对论性Vlasov-Maxwell系统的新延拓准则
DOI：
10.1007/s00220-014-2108-8
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发表时间：
2014
影响因子：
2.4
通讯作者：
S. Pankavich
中科院分区：
文献类型：
--
作者：
Charles Nguyen;J. Anderson;S. Pankavich
给定足够规则的有限能量初始数据，相对论性Vlasov-Maxwell系统解的整体存在性是一个长期存在的开放性问题。Glassey和Strauss （Arch Ration Mech Anal 92:59-90, 1986）的主要结果表明，只要f的动量支持保持有界，解（f， E， B）仍然是C1。后来Bouchut等人（Arch Ration Mech Anal 170:1-15, 2003）和Klainerman和Staffilani （common Pure apple Anal 1:103-125, 2002）给出了替代证明。我们证明，（f， E， B）在投射到任何二维平面后，只需要动量支持的有界性就可以保持C1。
The global existence of solutions to the relativistic Vlasov–Maxwell system given sufficiently regular finite energy initial data is a longstanding open problem. The main result of Glassey and Strauss (Arch Ration Mech Anal 92:59–90, 1986) shows that a solution (f, E, B) remains C1 as long as the momentum support of f remains bounded. Alternate proofs were later given by Bouchut et al. (Arch Ration Mech Anal 170:1–15, 2003) and Klainerman and Staffilani (Commun Pure Appl Anal 1:103–125, 2002). We show that only the boundedness of the momentum support of fafter projecting to any two dimensional plane is needed for (f, E, B) to remain C1.