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.
"A coupled system of Korteweg de Vries equations as singular limit of the Kuramoto-Sivashinsky equations." Adv. Differential Equations 12 (5) 541 - 572, 2007. https://doi.org/10.57262/ade/1367241436