Global Regularity and Scattering for General Non-Linear Wave Equations II. (4+1) Dimensional Yang--Mills Equations in the Lorentz Gauge

Abstract

We continue here with previous investigations on the global behavior of general type non-linear wave equations for a class of small, scale-invariant initial data. The method is based on the use of a new set of Strichartz estimates for the linear wave equation which incorporates extra weighted smoothness assumptions with respect to the angular variable, along with the construction of appropriate micro-local function spaces which take into account this type of additional regularity.