Advances in Differential Equations

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

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

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703299

Mathematical Reviews number (MathSciNet)
MR2816115

Zentralblatt MATH identifier
1228.35215

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

Citation

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. https://projecteuclid.org/euclid.ade/1355703299.


Export citation