# Almost sure scattering for the 4D energy-critical defocusing nonlinear wave equation with radial data

@article{Dodson2017AlmostSS,
title={Almost sure scattering for the 4D energy-critical defocusing nonlinear wave equation with radial data},
author={Benjamin Dodson and Jonas Luhrmann and Dana Mendelson},
journal={arXiv: Analysis of PDEs},
year={2017}
}
• Published 28 March 2017
• Mathematics
• arXiv: Analysis of PDEs
We consider the energy-critical defocusing nonlinear wave equation on $\mathbb{R}^4$ and establish almost sure global existence and scattering for randomized radially symmetric initial data in $H^s_x(\mathbb{R}^4) \times H^{s-1}_x(\mathbb{R}^4)$ for $\frac{1}{2} < s < 1$. This is the first almost sure scattering result for an energy-critical dispersive or hyperbolic equation with scaling super-critical initial data. The proof is based on the introduction of an approximate Morawetz estimate to…

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