Local smoothing for the Schrödinger equation with a prescribed loss

Hans Christianson, Jared Wunsch

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

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 Schrödinger 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.

Original languageEnglish (US)
Pages (from-to)1601-1632
Number of pages32
JournalAmerican Journal of Mathematics
Volume135
Issue number6
DOIs
StatePublished - Dec 2013

ASJC Scopus subject areas

  • Mathematics(all)

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