# The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions

@article{Killip2010TheRD,
title={The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions},
author={Rowan Killip and Monica Visan},
journal={arXiv: Analysis of PDEs},
year={2010}
}
• Published 9 February 2010
• Mathematics
• arXiv: Analysis of PDEs
We consider the defocusing nonlinear wave equation $u_{tt}-\Delta u + |u|^p u=0$ with spherically-symmetric initial data in the regime $\frac4{d-2} \frac4{d-2}$. The principal result is that blowup (or failure to scatter) must be accompanied by blowup of the critical Sobolev norm. An equivalent formulation is that maximal-lifespan solutions with bounded critical Sobolev norm are global and scatter.

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