Vol. 2, No. 2, 2020

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Dispersive estimates, blow-up and failure of Strichartz estimates for the Schrödinger equation with slowly decaying initial data

Rainer Mandel

Vol. 2 (2020), No. 2, 519–532
Abstract

The initial value problem for the homogeneous Schrödinger equation is investigated for radially symmetric initial data with slow decay rates and not too wild oscillations. Our global well-posedness results apply to initial data for which Strichartz estimates fail.

Keywords
Schrödinger equation, failure of Strichartz estimates, dispersive blow-up
Mathematical Subject Classification 2010
Primary: 35Q41
Secondary: 35B40, 35B44
Milestones
Received: 3 November 2019
Revised: 21 January 2020
Accepted: 21 February 2020
Published: 22 May 2020
Authors
Rainer Mandel
Karlsruhe Institute of Technology
Institute for Analysis
Karlsruhe
Germany