Vol. 1, No. 2, 2008

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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

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.

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