THE RADIAL DEFOCUSING ENERGY-SUPERCRITICAL NONLINEAR WAVE EQUATION IN ALL SPACE DIMENSIONS

被引：38
|
作者：
Killip, Rowan [1 ]
Visan, Monica [1 ]
机构：
[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 139卷 / 05期
基金：
美国国家科学基金会;
关键词：
GLOBAL WELL-POSEDNESS; KLEIN-GORDON EQUATION; SCHRODINGER-EQUATION; BLOW-UP; SCATTERING; REGULARITY; DECAY;
D O I：
10.1090/S0002-9939-2010-10615-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页码：1805 / 1817
页数：13
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