Vol. 5, No. 2, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 8, 1891–2146
Issue 7, 1643–1890
Issue 7, 1397–1644
Issue 6, 1397–1642
Issue 5, 1149–1396
Issue 4, 867–1148
Issue 3, 605–866
Issue 2, 259–604
Issue 1, 1–258

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
A bilinear oscillatory integral estimate and bilinear refinements to Strichartz estimates on closed manifolds

Zaher Hani

Vol. 5 (2012), No. 2, 339–363
Abstract

We prove a bilinear L2(d) × L2(d) L2(d+1) estimate for a pair of oscillatory integral operators with different asymptotic parameters and phase functions satisfying a transversality condition. This is then used to prove a bilinear refinement to Strichartz estimates on closed manifolds, similar to that derived by Bourgain on d, but at a relevant semiclassical scale. These estimates will be employed elsewhere to prove global well-posedness below H1 for the cubic nonlinear Schrödinger equation on closed surfaces.

Keywords
bilinear oscillatory integrals, bilinear Strichartz estimates, transversality, semiclassical time scale, nonlinear Schrödinger equation on compact manifolds
Mathematical Subject Classification 2000
Primary: 35B45, 42B20, 58J40
Secondary: 35A17, 35S30
Milestones
Received: 16 August 2010
Revised: 13 January 2011
Accepted: 13 February 2011
Published: 27 August 2012
Authors
Zaher Hani
Mathematics Department
University of California, Los Angeles
520 Portola Plaza, Math Sciences Building
Los Angeles, CA 90095
United States
http://www.math.ucla.edu/~zhani