## Advances in Operator Theory

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

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

#### 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