## Advances in Differential Equations

### A coupled system of Korteweg de Vries equations as singular limit of the Kuramoto-Sivashinsky equations

#### Abstract

We consider a coupled system of Kuramoto--Sivashinsky (KS) equations in a bounded interval depending on a suitable parameter $\nu > 0$. As $\nu$ tends to zero, we obtain a coupled system of Korteweg--de Vries (KdV) equations known to describe strong interactions of two long internal gravity waves in a stratified fluid. Existence and uniqueness of global solutions of the KS model is established as well.

#### Article information

Source
Adv. Differential Equations Volume 12, Number 5 (2007), 541-572.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1367241436

Mathematical Reviews number (MathSciNet)
MR2321565

Zentralblatt MATH identifier
1148.35078

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 76B55: Internal waves

#### Citation

Massarolo, C. P.; Menzala, G. P.; Pazoto, A. F. A coupled system of Korteweg de Vries equations as singular limit of the Kuramoto-Sivashinsky equations. Adv. Differential Equations 12 (2007), no. 5, 541--572.https://projecteuclid.org/euclid.ade/1367241436