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Applied Math Seminar Traveling Water Waves |
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This talk will describe an existence theorem for three dimensional traveling waves in the free surface of a body of water. The first such theorem in two dimensional settings is due to T. Levi-Civita and D. Struik in the 1920's. In a recent paper we have proved a general result for three (and higher) dimensions, when there is surface tension. The approach is surprisingly close to the Lyapunov center theorem of A. Weinstein, and the lower bound on the number of distinct solutions uses the Hamiltonian form for the water waves problem given by V.E. Zakharov. Without surface tension the problem exhibits small divisors, and is more difficult. |