# 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}
}
• Published 27 March 2014
• Mathematics
• Analysis & PDE
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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