Vol. 11, No. 4, 2018

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On a bilinear Strichartz estimate on irrational tori

Chenjie Fan, Gigliola Staffilani, Hong Wang and Bobby Wilson

Vol. 11 (2018), No. 4, 919–944
Abstract

We prove a bilinear Strichartz-type estimate for irrational tori via a decoupling-type argument, as used by Bourgain and Demeter (2015), recovering and generalizing a result of De Silva, Pavlović, Staffilani and Tzirakis (2007). As a corollary, we derive a global well-posedness result for the cubic defocusing NLS on two-dimensional irrational tori with data of infinite energy.

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Keywords
decoupling, bilinear Strichartz
Mathematical Subject Classification 2010
Primary: 35Q55, 42B37
Milestones
Received: 23 January 2017
Revised: 7 October 2017
Accepted: 11 December 2017
Published: 12 January 2018
Authors
Chenjie Fan
Department of Mathematics
University of Chicago
Chicago, IL
United States
Gigliola Staffilani
Department of Mathematics
Massachusetts Institue of Technology
Cambridge, MA
United States
Hong Wang
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Bobby Wilson
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States