Abstract:The mathematical study of travelling waves in the potential flow of two superposed layers of perfect fluid can be set as an illposed evolutionary problem, in which the horizontal unbounded space variable plays the role of "time". In this paper we consider two problems for which the bottom layer of fluid is infinitely deep: for the first problem, the upper layer is bounded by a rigid top and there is no surface tension at the interface; for the second problem, there is a free surface with a large enough surface… Show more
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