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2017 Construction of two-bubble solutions for the energy-critical NLS
Jacek Jendrej
Anal. PDE 10(8): 1923-1959 (2017). DOI: 10.2140/apde.2017.10.1923

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.

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Jacek Jendrej. "Construction of two-bubble solutions for the energy-critical NLS." Anal. PDE 10 (8) 1923 - 1959, 2017. https://doi.org/10.2140/apde.2017.10.1923

Information

Received: 7 November 2016; Revised: 8 May 2017; Accepted: 28 July 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1375.35492
MathSciNet: MR3694010
Digital Object Identifier: 10.2140/apde.2017.10.1923

Subjects:
Primary: 35B40

Keywords: energy-critical , multisoliton , nonlinear Schrödinger equation

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 8 • 2017
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