Scattering for the radial 3D cubic wave equation

@article{Dodson2015ScatteringFT,
  title={Scattering for the radial 3D cubic wave equation},
  author={Benjamin Dodson and Andrew Lawrie},
  journal={Analysis \& PDE},
  year={2015},
  volume={8},
  pages={467-497}
}
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 $\dot{H}^{\frac{1}{2}} \times \dot{H}^{-\frac{1}{2}}$ 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 scatter to free waves as $t \to \pm \infty$. 

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