The zero mass problem for Klein–Gordon equations

Abstract

In this paper, we are interested in the global existence result for a class of Klein–Gordon equations, particularly in the unified time decay result concerning a possibly vanishing mass parameter. We give for the first time a rigorous proof for this problem, which relies on both the flat foliation and the hyperboloidal foliation of the Minkowski spacetime. To take advantage of both foliations, an iteration procedure is used.