The Glassey conjecture on asymptotically flat manifolds
The Glassey conjecture on asymptotically flat manifolds
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DOI：
10.1090/s0002-9947-2014-06423-4
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发表时间：
2013-06
影响因子：
1.3
通讯作者：
Chengbo Wang
中科院分区：
文献类型：
--
作者：
Chengbo Wang
我们证明了渐近平坦流形$(R^{1+3}，g)$上的三维Glassey猜想，其中度量$g$是平坦度规的某个小时空扰动，以及非陷阱渐近欧氏流形。此外，对于径向渐近平坦流形$(R^{1+n}，g)$和$n\ge3$，我们在径向情形下验证了Glassey猜想。讨论了具有较高正则性的高维波动方程。其主要思想是利用变系数的局部能量估计和KSS估计，以及包括迹估计在内的加权Soblev估计。
We verify the 3-dimensional Glassey conjecture on asymptotically flat manifolds $(R^{1+3}, g)$, where the metric $g$ is certain small space-time perturbation of the flat metric, as well as the nontrapping asymptotically Euclidean manifolds. Moreover, for radial asymptotically flat manifolds $(R^{1+n}, g)$ with $n\ge 3$, we verify the Glassey conjecture in the radial case. High dimensional wave equations with higher regularity are also discussed. The main idea is to exploit local energy and KSS estimates with variable coefficients, together with the weighted Sobolev estimates including trace estimates.