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arXiv · 1902.08927

Global solution for Massive Maxwell-Klein-Gordon equations with large Maxwell field

Allen Fang·Qian Wang·Shiwu Yang
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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.

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Allen Fang, Qian Wang, Shiwu Yang. 2019-02-24. Global solution for Massive Maxwell-Klein-Gordon equations with large Maxwell field. https://arxiv.org/abs/1902.08927

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