Advances in Differential Equations

Well posedness for the 1D Zakharov-Rubenchik system

Felipe Linares and Carlos Matheus

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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

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

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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