Differential and Integral Equations

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

E. Compaan

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Abstract

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

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

Dates
First available in Project Euclid: 18 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1455806025

Mathematical Reviews number (MathSciNet)
MR3466167

Zentralblatt MATH identifier
06562177

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

Citation

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.


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