## Differential and Integral Equations

### A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equations in 2D

#### Abstract

We consider the initial value problem for a three-component system of quadratic nonlinear Schrödinger equations with mass resonance in two space dimensions. Under a suitable condition on the coefficients of the nonlinearity, we will show that the solution decays strictly faster than ${O(t^{-1})}$ as $t \to +\infty$ in $L^{\infty}$ by providing an enhanced decay estimate of order $O((t\log t)^{-1})$. Differently from the previous works, our approach does not rely on the explicit form of the asymptotic profile of the solution at all.

#### Article information

Source
Differential Integral Equations, Volume 27, Number 3/4 (2014), 301-312.

Dates
First available in Project Euclid: 30 January 2014

https://projecteuclid.org/euclid.die/1391091368

Mathematical Reviews number (MathSciNet)
MR3161606

Zentralblatt MATH identifier
1324.35170

#### Citation

Katayama, Soichiro; Li, Chunhua; Sunagawa, Hideaki. A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equations in 2D. Differential Integral Equations 27 (2014), no. 3/4, 301--312. https://projecteuclid.org/euclid.die/1391091368