Global stability for charged-scalar fields on Minkowski space

Abstract

We prove that the charged-scalar-field equations are globally stable on (3+1)-dimensional Minkowski space for small initial data in certain gauge covariant weighted Sobolev spaces. These spaces can be chosen to be almost scale invariant with respect to the homogeneity of the equations, and our result is valid for initial data with nonzero charge that is also nonstationary at space-like infinity. The method of proof is a tensor-geometric approach which is based on a sharp family of weighted bilinear L2 space-time estimates.