Advances in Operator Theory

Well-posedness issues for a class of coupled nonlinear Schrödinger equations with critical exponential growth

Hanen Hezzi

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Abstract

The initial value problem for some coupled nonlinear Schrödinger equations in two space dimensions with exponential growth is investigated. In the defocusing case, global well-posedness and scattering are obtained. In the focusing sign, global and nonglobal existence of solutions are discussed via potential well-method.

Article information

Source
Adv. Oper. Theory, Volume 3, Number 3 (2018), 551-581.

Dates
Received: 7 September 2017
Accepted: 7 February 2018
First available in Project Euclid: 3 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.aot/1520046045

Digital Object Identifier
doi:10.15352/aot.1709-1227

Mathematical Reviews number (MathSciNet)
MR3795100

Zentralblatt MATH identifier
1393.35222

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35Q41: Time-dependent Schrödinger equations, Dirac equations

Keywords
nonlinear Schrödinger system global well-posedness scattering blow-up Moser–Trudinger inequality

Citation

Hezzi, Hanen. Well-posedness issues for a class of coupled nonlinear Schrödinger equations with critical exponential growth. Adv. Oper. Theory 3 (2018), no. 3, 551--581. doi:10.15352/aot.1709-1227. https://projecteuclid.org/euclid.aot/1520046045


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