Global well-posedness and scattering for the radial, defocusing, cubic wave equation with initial data in a critical Besov space

Abstract

In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in $B_{1,1}^2\times B_{1,1}^1$. This space of functions is a scale invariant subspace of ${\dot{H}}^{1/2}\times {\dot{H}}^{-1/2}$.

28 pages