Differential and Integral Equations

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

Chunhua Li

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1423055224

Mathematical Reviews number (MathSciNet)
MR3306559

Zentralblatt MATH identifier
1363.35345

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

Citation

Li, Chunhua. On a system of quadratic nonlinear Schrödinger equations and scale invariant spaces in 2D. Differential Integral Equations 28 (2015), no. 3/4, 201--220. https://projecteuclid.org/euclid.die/1423055224


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