## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 437 - 444

### Further decay results on the system of NLS equations in lower order Sobolev spaces

#### Abstract

The initial value problem of a system of nonlinear Schrödinger equations with quadratic nonlinearities in two space dimensions is studied. We show there exists a unique global solution for this initial value problem which decays like $t^{-1}$ as $t\to +\infty$ in $\mathbf{L}^\infty (\mathbb{R}^2)$ for small initial data in lower order Sobolev spaces.

#### Article information

**Dates**

Received: 8 December 2011

Revised: 3 February 2012

First available in Project Euclid:
30 October 2018

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1540934241

**Digital Object Identifier**

doi:10.2969/aspm/06410437

**Mathematical Reviews number (MathSciNet)**

MR3381310

**Zentralblatt MATH identifier**

1335.35235

**Subjects**

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

**Keywords**

A system of nonlinear Schrödinger equations $L^\infty (\mathbb{R}^2)$-time decay estimates

#### Citation

Li, Chunhua. Further decay results on the system of NLS equations in lower order Sobolev spaces. Nonlinear Dynamics in Partial Differential Equations, 437--444, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410437. https://projecteuclid.org/euclid.aspm/1540934241