A note on coupled nonlinear Schrödinger equations

Abstract

We investigate the initial value problem for some coupled nonlinear Schrödinger equations in two space dimensions with exponential growth. We prove global well-posedness and scattering in the defocusing case. In the focusing sign, existence of non-global solution is discussed via the potential-well theory.

Keywords

• nonlinear schrödinger system
• global well-posedness
• scattering
• blow-up
• moser–trudinger inequality
• 35q55