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arXiv · 1002.1756

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

Rowan Killip·Monica Visan
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Abstract

We consider the defocusing nonlinear wave equation $u_{tt}-Δu + |u|^p u=0$ 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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Rowan Killip, Monica Visan. 2010-02-09. The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions. https://arxiv.org/abs/1002.1756

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