@article{22061,
  abstract     = {We consider the defocusing nonlinear wave equation utt − Δu +
|u|
pu = 0 with spherically-symmetric initial data in the regime 4
d−2 <p< 4
d−3
(which is energy-supercritical) and dimensions 3 ≤ d ≤ 6; we also consider
d ≥ 7, but for a smaller range of p> 4
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},
  author       = {Killip, Rowan and Visan, Monica},
  issn         = {1088-6826},
  journal      = {Proceedings of the American Mathematical Society},
  number       = {5},
  pages        = {1805--1817},
  publisher    = {American Mathematical Society},
  title        = {{The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions}},
  doi          = {10.1090/s0002-9939-2010-10615-9},
  volume       = {139},
  year         = {2011},
}