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

In the author’s previous work, it has been shown that solutions of Maxwell–Klein–Gordon equations in [math] 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.