论文标题
共形扰动和局部平滑
Conformal Perturbations and Local Smoothing
论文作者
论文摘要
本文的目的是研究保形扰动对施罗丁方程对革命表面的局部平滑作用的影响。论文\ cite {chwu-lsm}用一个被困的轨道研究了革命表面上的schrödinger方程。该捕获附近的动态是不稳定的，但是堕落的。从本文的公制$ g $开始，我们考虑了扰动的度量$ g_s = e^{sf} g $，其中$ f $是一个平稳，紧凑的功能。如果$ s $足够小且有限的$ f $衍生品满足适当的符号估计，那么我们表明当地的平滑估算仍然存在。
The purpose of this paper is to study the effect of conformal perturbations on the local smoothing effect for the Schrödinger equation on surfaces of revolution. The paper \cite{ChWu-lsm} studied the Schrödinger equation on surfaces of revolution with one trapped orbit. The dynamics near this trapping were unstable, but degenerately so. Beginning from the metric $g$ from this paper, we consider the perturbed metric $g_s = e^{sf}g$, where $f$ is a smooth, compactly supported function. If $s$ is small enough and finitely many derivatives of $f$ satisfy appropriate symbolic estimates, then we show that a local smoothing estimate still holds.
