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A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation

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  • The Benjamin-Ono equation is known as a model of internal long waves in stratified fluids or two-fluid systems. In this paper, we consider the validity of this type of modeling of a two-phase problem for capillary-gravity waves, which is a free boundary problem for the incompressible Euler equation with the irrotational condition. We show that the solutions of the free boundary problem split up into two waves and the shape of each wave is governed by the Benjamin-Ono equation in a slow time scale.
    Mathematics Subject Classification: Primary: 35Q35, 35Q53; Secondary: 76B55, 76B07.


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