Modification of the vector-field method related to quadratically perturbed wave equations in two space dimensions

Abstract

The purpose of this paper is to shed light on the fact that the global solvability for the quadratically perturbed wave equation with small initial data in two space dimension can be shown by using only a restricted set of vector fields associated with the space-time translation and spatial rotations. As a by-product, we establish almost best possible decay estimates related to the above vector fields, as well as the tangential derivatives to the forward light cones.