Resolvent Estimates for Normally Hyperbolic Trapped Sets

Jared Wunsch*, Maciej Zworski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Scopus citations

Abstract

We give pole free strips and estimates for resolvents of semiclassical operators which, on the level of the classical flow, have normally hyperbolic smooth trapped sets of codimension two in phase space. Such trapped sets are structurally stable and our motivation comes partly from considering the wave equation for Kerr black holes and their perturbations, whose trapped sets have precisely this structure. We give applications including local smoothing effects with epsilon derivative loss for the Schrödinger propagator as well as local energy decay results for the wave equation.

Original languageEnglish (US)
Pages (from-to)1349-1385
Number of pages37
JournalAnnales Henri Poincare
Volume12
Issue number7
DOIs
StatePublished - Nov 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

Fingerprint

Dive into the research topics of 'Resolvent Estimates for Normally Hyperbolic Trapped Sets'. Together they form a unique fingerprint.

Cite this