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.
Citation
C. P. Massarolo. G. P. Menzala. A. F. Pazoto. "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
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