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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 |
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Vol. 1 (2008), No. 2, 229–266
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Abstract |
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We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation for large spherically symmetric initial data in dimensions . 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
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Mathematical Subject Classification 2000
Primary: 35Q55
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Milestones
Received: 11 August 2008
Revised: 20 August 2008
Accepted: 23 September 2008
Published: 29 June 2009
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Authors |
| Rowan Killip | |
| 520 Portola Plaza Math Sciences Building 6363 Mailcode: 155505 Los Angeles, CA 90095 United States |
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| http://www.math.ucla.edu/~killip/ | |
| Monica Visan | |
| Department of Mathematics University of Chicago 5734 University Avenue Chicago, IL 60637-1514 United States |
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| http://www.math.uchicago.edu/~mvisan/ | |
| Xiaoyi Zhang | |
| School of Mathematics Institute for Advanced Study One Einstein Drive Princeton, NJ 08540 United States |
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