Advanced Studies in Pure Mathematics

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

Chunhua Li

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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

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

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


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