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Construction of
two-bubble solutions for the energy-critical NLS
Jacek Jendrej |
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Vol. 10 (2017), No. 8, 1923–1959
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Abstract |
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We construct pure two-bubbles for the energy-critical focusing nonlinear Schrödinger equation in space dimension . The constructed solution is global in (at least) one time direction and approaches a superposition of two stationary states both centered at the origin, with the ratio of their length scales converging to . One of the bubbles develops at scale , whereas the length scale of the other converges to at rate . The phases of the two bubbles form the right angle. |
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Keywords
nonlinear Schrödinger equation, energy-critical,
multisoliton
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Mathematical Subject Classification 2010
Primary: 35B40
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Milestones
Received: 7 November 2016
Revised: 8 May 2017
Accepted: 28 July 2017
Published: 18 August 2017
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Authors |
| Jacek Jendrej | |
| Department of Mathematics University of Chicago Chicago, IL % 60615 United States |
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