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

Abstract

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 ${Ḣ}^{1∕2}\times {Ḣ}^{-1∕2}$.