Vol. 10, No. 8, 2017

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Construction of two-bubble solutions for the energy-critical NLS

Jacek Jendrej

Vol. 10 (2017), No. 8, 1923–1959
Abstract

We construct pure two-bubbles for the energy-critical focusing nonlinear Schrödinger equation in space dimension N 7. 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 0. One of the bubbles develops at scale 1, whereas the length scale of the other converges to 0 at rate |t| 2 N6 . The phases of the two bubbles form the right angle.

Keywords
nonlinear Schrödinger equation, energy-critical, multisoliton
Mathematical Subject Classification 2010
Primary: 35B40
Milestones
Received: 7 November 2016
Revised: 8 May 2017
Accepted: 28 July 2017
Published: 18 August 2017
Authors
Jacek Jendrej
Department of Mathematics
University of Chicago
Chicago, IL
% 60615
United States