The decay of solutions of Maxwell-Klein-Gordon equations

It has been shown that there are global solutions to 
Maxwell-Klein-Gordon equations in Minkowski space with finite energy 
data. However, very little is known about the asymptotic behavior of the 
solution. In this talk, I will present recent progress on the decay 
properties of the solutions. We show the quantitative energy flux decay 
of the solutions with data merely bounded in some weighted energy space. 
The results in particular hold in the presence of large total charge. 
This is the first result that gives a complete and precise description 
of the global behavior of large nonlinear fields.