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

#### 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