Cambridge Journal of Mathematics

Volume 7 (2019)

Number 4

On global dynamics of the Maxwell–Klein–Gordon equations

Pages: 365 – 467



Shiwu Yang (Beijing International Center for Mathematical Research, Peking University, Beijing, China)

Pin Yu (Department of Mathematics and Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)


On the three dimensional Euclidean space, for data with finite energy, it is well-known that the Maxwell–Klein–Gordon equations admit global solutions. However, the asymptotic behavior of the solutions for the data with non-vanishing charge and arbitrary large size is unknown. It is conjectured that the solutions disperse as linear waves and enjoy the so-called peeling properties for pointwise estimates.We provide a gauge independent proof of the conjecture.


Maxwell–Klein–Gordon equations, peeling estimates, large data

2010 Mathematics Subject Classification

Primary 35L05, 35Q75. Secondary 35Q60.

The first-named author is partially supported by the Recruitment Program of Global Experts in China and a start-up grant at Peking University.

The second-named author is supported by NSFC-11522111, NSFC-11825103 and China National Support Program for Young Top-Notch Talents.

Received 25 February 2019

Published 1 November 2019