Advances in Differential Equations

Well posedness for the 1D Zakharov-Rubenchik system

Felipe Linares and Carlos Matheus

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Abstract

Local and global well posedness results are established for the initial-value problem associated to the 1D Zakharov-Rubenchik system. We show that our results are sharp in some situations by proving ill-posedness results otherwise. The global results allow us to study the norm growth of solutions corresponding to the Schrödinger equation term. We use ideas recently introduced to study the classical Zakharov systems.

Article information

Source
Adv. Differential Equations Volume 14, Number 3/4 (2009), 261-288.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867267

Mathematical Reviews number (MathSciNet)
MR2493563

Zentralblatt MATH identifier
1165.35448

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Linares, Felipe; Matheus, Carlos. Well posedness for the 1D Zakharov-Rubenchik system. Adv. Differential Equations 14 (2009), no. 3/4, 261--288. https://projecteuclid.org/euclid.ade/1355867267.


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