Local Smoothing Estimates near a Trapped Set with Infinitely Many Connected Components

2014/12/19 by Hans Christianson, Christianson, Hans, Dylan Muckerman +1
Computer Science · Mathematics · #35B34 #35S05 #47A10 #58J50 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1412.6389

openalex publication_date 2014/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a local smoothing result for the Schrödinger equation on a class of surfaces of revolution which have infinitely many trapped geodesics. Our main result is a local smoothing estimate with loss (compared to \citeChMe-lsm) depending on the accumulation rate of the critical points of the profile curve. The proof uses an h-dependent version of semiclassical propagation of singularities, and a result on gluing an h-dependent number of cutoff resolvent estimates.

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