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arXiv 1503.01562math.AP
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(4+1)维Maxwell-Klein-Gordon方程的整体适定性与散射性

Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation

Sung-Jin Oh, Daniel Tataru

摘要:

本文是三篇论文序列的最后一部分,其目的是证明能量临界Maxwell-Klein-Gordon方程(MKG)在$\mathbb{R}^{1+4}$上的全局适定性和分散性,对于任意有限能量的初始数据.利用在前两篇论文中建立的连续更强的延拓/散射准则,我们进行了爆破分析,并推导出整体适定性和散射的失败意味着存在一个非平凡的平稳或自相似的解决方案MKG。然后,通过确定这样的解不存在,我们完成了证明。

英文摘要:

This article constitutes the final and main part of a three-paper sequence, whose goal is to prove global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon equation (MKG) on $\mathbb{R}^{1+4}$ for arbitrary finite energy initial data. Using the successively stronger continuation/scattering criteria established in the previous two papers, we carry out a blow-up analysis and deduce that the failure of global well-posedness and scattering implies the existence of a nontrivial stationary or self-similar solution to MKG. Then, by establishing that such solutions do not exist, we complete the proof.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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