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April 2020 Scattering for the mass super-critical perturbations of the mass critical nonlinear Schrödinger equations
Xing Cheng
Illinois J. Math. 64(1): 21-48 (April 2020). DOI: 10.1215/00192082-8165582

Abstract

We consider the Cauchy problem for the nonlinear Schrödinger (NLS) equation with double nonlinearities with opposite sign, with one term mass-critical and the other term mass-supercritical and energy-subcritical, which includes the well-known two-dimensional cubic-quintic NLS equation arising in the study of the boson gas with 2- and 3-body interactions. We prove global well-posedness and scattering in H1(Rd) below the threshold for nonradial data when 1d4.

Citation

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Xing Cheng. "Scattering for the mass super-critical perturbations of the mass critical nonlinear Schrödinger equations." Illinois J. Math. 64 (1) 21 - 48, April 2020. https://doi.org/10.1215/00192082-8165582

Information

Received: 17 November 2018; Revised: 2 October 2019; Published: April 2020
First available in Project Euclid: 6 March 2020

zbMATH: 07179188
MathSciNet: MR4072640
Digital Object Identifier: 10.1215/00192082-8165582

Subjects:
Primary: 35Q55
Secondary: 35L70

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 1 • April 2020
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