Advances in Differential Equations

Well posedness and stability in the periodic case for the Benney system

J. Angulo, A.J. Corcho, and S. Hakkaev

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We establish local well-posedness results in weak periodic function spaces for the Cauchy problem of the Benney system. The Sobolev space $H^{1/2}\times L^2$ is the lowest regularity attained and also we cover the energy space $H^{1}\times L^2$, where global well posedness follows from the conservation laws of the system. Moreover, we show the existence of a smooth explicit family of periodic travelling waves of dnoidal type and we prove, under certain conditions, that this family is orbitally stable in the energy space.

Article information

Adv. Differential Equations, Volume 16, Number 5/6 (2011), 523-550.

First available in Project Euclid: 17 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35Q60: PDEs in connection with optics and electromagnetic theory


Angulo, J.; Corcho, A.J.; Hakkaev, S. Well posedness and stability in the periodic case for the Benney system. Adv. Differential Equations 16 (2011), no. 5/6, 523--550.

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