Steady Water Waves

Abstract

The classical water wave problem concerns the irrotational flow of a perfect fluid of unit density subject to the forces of gravity and surface tension. The fluid motion is described by the Euler equations in a domain bounded below by a rigid horizontal bottom {y = −h} and above by a free surface which is described as a graph {y = η(x, z, t)}, where the function η depends upon the two horizontal spatial directions x, z and time t. In terms of an Eulerian velocity potential φ(x, y, z, t) the mathematical problem is to solve the equations

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Cite this paper

@inproceedings{Groves2004SteadyWW, title={Steady Water Waves}, author={Mark D. Groves}, year={2004} }