Decay of solutions for a system of nonlinear Schrödinger equations in 2D

Chunhua Li

doi:10.3934/dcds.2012.32.4265

Article Contents

2012, Volume 32, Issue 12: 4265-4285. Doi: 10.3934/dcds.2012.32.4265

This issue Previous Article Semilinear elliptic systems involving multiple critical exponents and singularities in $\mathbb{R}^N$ Next Article Some results on perturbations of Lyapunov exponents

Decay of solutions for a system of nonlinear Schrödinger equations in 2D

Chunhua Li^1,

1.
Department of Mathematics, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043

Received: May 31, 2011

Revised: July 31, 2011

Published: November 2012

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Abstract

We deal with a system of nonlinear Schrödinger equations with quadratic nonlinearities in two space dimensions. We prove $\mathbf{L}^{\infty }-$time decay estimates of small solutions. We also discuss existence and nonexistence of wave operators.

Keywords:

A system of nonlinear Schrödinger equations,
$L^{\infty }$-time decay estimates,
wave operators.

Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B40.

Citation:

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References

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