Vol. 1, No. 2, 2008

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

Volume 17
Issue 9, 2997–3369
Issue 8, 2619–2996
Issue 7, 2247–2618
Issue 6, 1871–2245
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher

Rowan Killip, Monica Visan and Xiaoyi Zhang

Vol. 1 (2008), No. 2, 229–266
Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut + Δu = ±|u|4du for large spherically symmetric Lx2(d) initial data in dimensions d 3. In the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.

Keywords
Nonlinear Schrödinger equation, mass-critical, focusing
Mathematical Subject Classification 2000
Primary: 35Q55
Milestones
Received: 11 August 2008
Revised: 20 August 2008
Accepted: 23 September 2008
Published: 29 June 2009
Authors
Rowan Killip
520 Portola Plaza
Math Sciences Building 6363
Mailcode: 155505
Los Angeles, CA 90095
United States
http://www.math.ucla.edu/~killip/
Monica Visan
Department of Mathematics
University of Chicago
5734 University Avenue
Chicago, IL 60637-1514
United States
http://www.math.uchicago.edu/~mvisan/
Xiaoyi Zhang
School of Mathematics
Institute for Advanced Study
One Einstein Drive
Princeton, NJ 08540
United States