#### Vol. 12, No. 4, 2019

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

### Benjamin Dodson

Vol. 12 (2019), No. 4, 1023–1048
DOI: 10.2140/apde.2019.12.1023
##### Abstract

We prove that the cubic wave equation is globally well-posed and scattering for radial initial data lying in ${B}_{1,1}^{2}×{B}_{1,1}^{1}$. This space of functions is a scale-invariant subspace of ${Ḣ}^{1∕2}×{Ḣ}^{-1∕2}$.

##### Keywords
defocusing, nonlinear wave equation, scattering, global well-posedness
##### Mathematical Subject Classification 2010
Primary: 35L05, 35B40