#### Vol. 8, No. 2, 2015

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Scattering for the radial 3D cubic wave equation

### Benjamin Dodson and Andrew Lawrie

Vol. 8 (2015), No. 2, 467–497
##### Abstract

Consider the Cauchy problem for the radial cubic wave equation in $1+3$ dimensions with either the focusing or defocusing sign. This problem is critical in ${Ḣ}^{1∕2}×{Ḣ}^{-1∕2}\left({ℝ}^{3}\right)$ and subcritical with respect to the conserved energy. Here we prove that if the critical norm of a solution remains bounded on the maximal time interval of existence, then the solution must in fact be global in time and must scatter to free waves as $t\to ±\infty$.

##### Keywords
scattering, concentration compactness, double Duhamel
Primary: 35L05