论文标题
在多核产品歧管上，schrödinger方程的局部平滑，带有拐点传输捕获
Local Smoothing for the Schrödinger Equation on a Multi-Warped Product Manifold with Inflection-Transmission Trapping
论文作者
论文摘要
测量诱捕是对Schrödinger方程解决方案的分散估计的阻碍。令人惊讶的是，关于schrödinger方程的解决方案在具有退化捕获的歧管上的解决方案知之甚少，因为在扰动下，退化捕获的条件不稳定。在本文中，我们将[CM14]的一些结果扩展到扭曲产品歧管上的拐点传输类型上的一些结果到多磁产品的情况。主要结果是，一个横截面上的陷阱不会与其他横截面上的陷阱相互作用，前提是歧管只有一个无限端，只有拐点传输类型捕获。
Geodesic trapping is an obstruction to dispersive estimates for solutions to the Schrödinger equation. Surprisingly little is known about solutions to the Schrödinger equation on manifolds with degenerate trapping, since the conditions for degenerate trapping are not stable under perturbations. In this paper we extend some of the results of [CM14] on inflection-transmission type trapping on warped product manifolds to the case of multi-warped products. The main result is that the trapping on one cross section does not interact with the trapping on other cross sections provided the manifold has only one infinite end and only inflection-transmission type trapping.
