Differential and Integral Equations

Local and global solutions for the non-linear Schrödinger-Boussinesq system

Luiz Gustavo Farah

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Abstract

We study the local and global well posedness of the initial-value problem for the non-linear Schrödinger-Boussinesq System. Local existence results are proved for three initial data in Sobolev spaces of negative indices. Global results are proved using the arguments of Colliander Holmer and Tzirakis (2006 Arxiv preprint math.AP/0603595).

Article information

Source
Differential Integral Equations, Volume 21, Number 7-8 (2008), 743-770.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356038621

Mathematical Reviews number (MathSciNet)
MR2479690

Zentralblatt MATH identifier
1224.35027

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Citation

Farah, Luiz Gustavo. Local and global solutions for the non-linear Schrödinger-Boussinesq system. Differential Integral Equations 21 (2008), no. 7-8, 743--770. https://projecteuclid.org/euclid.die/1356038621


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