Global solution for Massive Maxwell-Klein-Gordon equations with large Maxwell field
Abstract
We derive the global dynamic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field) with a general, unrestrictive class of data, in particular, for Maxwell field of arbitrary size, and by a gauge independent method. Due to the critical slow decay expected for the Maxwell field, the scalar field exhibits a loss of decay at the causal infinities within an outgoing null cone. To overcome the difficulty caused by such loss in the energy propagation, we uncover a hidden cancellation contributed by the Maxwell equation, which enables us to obtain the sharp control of the Maxwell field under a rather low regularity assumption on data. Our method can be applied to other physical field equations, such as the Einstein equations for which a similar cancellation structure can be observed.
Cite
@article{arxiv.1902.08927,
title = {Global solution for Massive Maxwell-Klein-Gordon equations with large Maxwell field},
author = {Allen Fang and Qian Wang and Shiwu Yang},
journal= {arXiv preprint arXiv:1902.08927},
year = {2019}
}