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

We derive the global dynamic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field) with a general 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.

Automated summary

The authors derive the global dynamic properties of the mMKG system with a general class of data, particularly for Maxwell fields of arbitrary size, by using a gauge independent method. Despite the expected critical slow decay of the Maxwell field, the scalar field experiences a loss of decay at causal infinities within an outgoing null cone. Through uncovering a hidden cancellation contributed by the Maxwell equation, the authors are able to obtain precise control of the Maxwell field under low regularity assumptions on data. This method may also be applicable to other physical field equations, such as the Einstein equations, where a similar cancellation structure can be observed.