Local smoothing for the Schrödinger equation with a prescribed loss
Local smoothing for the Schrödinger equation with a prescribed loss
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具有指定损失的薛定谔方程的局部平滑
DOI：
10.1353/ajm.2013.0047
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发表时间：
2011
影响因子：
1.7
通讯作者：
J. Wunsch
中科院分区：
文献类型：
--
作者：
H. Christianson;J. Wunsch
我们考虑一个家庭的表面的革命，每一个单一的周期测地线是退化不稳定的。我们证明了一个局部光滑估计的线性薛定谔方程的损失，取决于退化的解决方案，我们构造明确的例子来表明我们的估计是饱和的弱半经典时间尺度。作为我们的证明的副产品，我们得到了一个尖锐的多项式损失的截止预解估计。
We consider a family of surfaces of revolution, each with a single periodic geodesic which is degenerately unstable. We prove a local smoothing estimate for solutions to the linear Schrodinger equation with a loss that depends on the degeneracy, and we construct explicit examples to show our estimate is saturated on a weak semiclassical time scale. As a byproduct of our proof, we obtain a cutoff resolvent estimate with a sharp polynomial loss.