Cambridge Journal of Mathematics
Volume 7 (2019)
On global dynamics of the Maxwell–Klein–Gordon equations
Pages: 365 – 467
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