##### Department of Mathematics,

University of California San Diego

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### Mathematics Colloquium

## Walter Craig

#### McMaster University

## Traveling water waves

##### Abstract:

I will describe an existence theorem for traveling waves in water. Thisis aproblem of the dynamics of a free surface of an incompressible fluid.The first suchresult in two dimensional settings is due to T. Levi-Civita and D.Struik in the 1920's.In a recent paper we prove a general result for three dimensions (well,for anynumber of dimensions), when there is surface tension. The approach issurprisinglyclose to the Lyapunov center theorem of A. Weinstein, using the fact due toV. E. Zakharov that the water waves problem is a Hamiltonian system.Withoutsurface tension the problem exhibits small divisors, and is more difficult.

Host: Hans Lindblad

### November 7, 2002

### 3:00 PM

### AP&M 6438

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