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

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

2010-02-09

arxiv.org/abs/1002.1756v1

Mathematics

Analysis of PDEs

Scientific paper

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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