Differential and Integral Equations

Smoothing and global attractors for the Majda-Biello system on the torus

E. Compaan

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


In this paper, we consider the Majda-Biello system, a coupled KdV-type system, on the torus. In the first part of the paper, it is shown that, given initial data in a Sobolev space, the difference between the linear and the nonlinear evolution almost always resides in a smoother space. The smoothing index depends on number-theoretic properties of the coupling parameter in the system which control the behavior of the resonant sets. In the second part of the paper, we consider the forced and damped version of the system and obtain similar smoothing estimates. These estimates are used to show the existence of a global attractor in the energy space. We also show that when the damping is large in relation to the forcing terms, the attractor is trivial.

Article information

Differential Integral Equations, Volume 29, Number 3/4 (2016), 269-308.

First available in Project Euclid: 18 February 2016

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35B41: Attractors


Compaan, E. Smoothing and global attractors for the Majda-Biello system on the torus. Differential Integral Equations 29 (2016), no. 3/4, 269--308. https://projecteuclid.org/euclid.die/1455806025

Export citation