## Differential and Integral Equations

### On a system of quadratic nonlinear Schrödinger equations and scale invariant spaces in 2D

Chunhua Li

#### Abstract

We consider the initial value problem of a system of 2D nonlinear Schrödinger equations with quadratic nonlinearities in homogeneous Sobolev spaces which are close to the scale invariant spaces. We show the global solution, which is not necessarily in $\mathbf{L}^{2}( \mathbb{R}^{2})$, satisfies uniform time decay of order $|t|^{-1}$ in $\mathbf{L}^{\infty }( \mathbb{R}^{2})$.

#### Article information

Source
Differential Integral Equations, Volume 28, Number 3/4 (2015), 201-220.

Dates
First available in Project Euclid: 4 February 2015