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

Yang, Shiwu

doi:10.2140/apde.2016.9.1829

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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

DOI: 10.2140/apde.2016.9.1829

Abstract

In the author’s previous work, it has been shown that solutions of Maxwell–Klein–Gordon equations in $ℝ^{3 + 1}$ 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.

Keywords

Maxwell–Klein–Gordon, decay

Mathematical Subject Classification 2010

Primary: 35Q61

Milestones

Received: 1 November 2015

Revised: 7 March 2016

Accepted: 28 August 2016

Published: 11 December 2016

Authors

Shiwu Yang
Beijing International Center for Mathematical Research Peking University Beijing 100086 China

Vol. 9, No. 8, 2016