Differential and Integral Equations

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

Soichiro Katayama, Chunhua Li, and Hideaki Sunagawa

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1391091368

Mathematical Reviews number (MathSciNet)
MR3161606

Zentralblatt MATH identifier
1324.35170

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35B40: Asymptotic behavior of solutions

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


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