Strichartz estimates for the Schrödinger flow on compact Lie groups

Zhang, Yunfeng

doi:10.2140/apde.2020.13.1173

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Strichartz estimates for the Schrödinger flow on compact Lie groups

Yunfeng Zhang

Vol. 13 (2020), No. 4, 1173–1219

DOI: 10.2140/apde.2020.13.1173

Abstract

We establish scale-invariant Strichartz estimates for the Schrödinger flow on any compact Lie group equipped with canonical rational metrics. In particular, full Strichartz estimates without loss for some nonrectangular tori are given. The highlights of this paper include estimates for some Weyl-type sums defined on rational lattices, different decompositions of the Schrödinger kernel that accommodate different positions of the variable inside the maximal torus relative to the cell walls, and an application of the BGG-Demazure operators or Harish-Chandra’s integral formula to the estimate of the difference between characters.

Keywords

compact Lie groups, Schrödinger equation, circle method, Strichartz estimates, BGG-Demazure operators, Harish-Chandra's integral formula

Mathematical Subject Classification 2010

Primary: 42B37

Secondary: 22E30

Milestones

Received: 27 August 2018

Revised: 19 February 2019

Accepted: 18 April 2019

Published: 13 June 2020

Authors

Yunfeng Zhang
Department of Mathematics University of Connecticut Storrs, CT United States

Vol. 13, No. 4, 2020