On the fourth order Schrödinger equation in three dimensions: Dispersive estimates and zero energy resonances

M. Burak Erdoğan, William R. Green, Ebru Toprak

Research output: Contribution to journalArticle

Abstract

We study the fourth order Schrödinger operator H=(−Δ)2+V for a short range potential in three space dimensions. We provide a full classification of zero energy resonances and study the dynamic effect of each on the L1→L dispersive bounds. In all cases, we show that the natural [Formula presented] decay rate may be attained, though for some resonances this requires subtracting off a finite rank term, which we construct and analyze. The classification of these resonances, as well as their dynamical consequences differ from the Schrödinger operator −Δ+V.

Original languageEnglish (US)
Pages (from-to)152-185
Number of pages34
JournalJournal of Differential Equations
Volume271
DOIs
StatePublished - Jan 15 2021

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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