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

• 成果类型: Article
• 署名作者: Oh, Sung-Jin; Tataru, Daniel
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0646-8
• 发表日期: 2016
• 页码: 781-877
• 关键词: yang-mills equations; nonlinear-wave equations; critical sobolev norm; finite-energy; local existence; maps equation; blow-up; REGULARITY; dimensions; SYSTEM

摘要

This article constitutes the final and main part of a three-paper sequence (Ann PDE, 2016. doi:10.1007/s40818-016-0006-4; Oh and Tataru, 2015. arXiv:1503.01561), whose goal is to prove global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon equation (MKG) on R1+4 for arbitrary finite energy initial data. Using the successively stronger continuation/scattering criteria established in the previous two papers (Ann PDE, 2016. doi:10.1007/s40818-016-0006-4; Oh and Tataru, 2015. arXiv: 1503.01561), 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.