Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 139, Issue 5, Pages 1805-1817Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9939-2010-10615-9
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Funding
- NSF [DMS-0701085, DMS-0901166]
- Direct For Mathematical & Physical Scien [0965029] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [0965029] Funding Source: National Science Foundation
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We consider the defocusing nonlinear wave equation u(tt) - Delta u + vertical bar u vertical bar(p)u = 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.
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