Vol. 9, No. 8, 2016

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Decay of solutions of Maxwell–Klein–Gordon equations with arbitrary Maxwell field

Shiwu Yang

Vol. 9 (2016), No. 8, 1829–1902

In the author’s previous work, it has been shown that solutions of Maxwell–Klein–Gordon equations in 3+1 possess some form of global strong decay properties with data bounded in some weighted energy space. In this paper, we prove pointwise decay estimates for the solutions for the case when the initial data are merely small on the scalar field but can be arbitrarily large on the Maxwell field. This extends the previous result of Lindblad and Sterbenz, in which smallness was assumed both for the scalar field and the Maxwell field.

Maxwell–Klein–Gordon, decay
Mathematical Subject Classification 2010
Primary: 35Q61
Received: 1 November 2015
Revised: 7 March 2016
Accepted: 28 August 2016
Published: 11 December 2016
Shiwu Yang
Beijing International Center for Mathematical Research
Peking University
Beijing 100086