##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Vera Mikyoung Hur

#### Massachusetts Institute of Technology

## Dispersive Properties of the Surface Water-Wave Problem

##### Abstract:

I will speak on the dispersive character of waves on the interface between vacuum and water under the influence of gravity and surface tension. I will begin by giving a preciese account of the formulation of the surface water-wave problem and discusion of its distinct features. They include the dispersion relation, its severe nonlinearity, traveling waves and the Hamiltonian structure. I will describe the recent work of Hans Christianson, Gigliola Staffilani and myself on the local smoothing effect of 1/4 derivative for the fully nonlinear problem under surface tension with some detail of the proof. If time permits, I will explore some oen questions regarding long-time behavior and stability.

Host: Peter Ebenfelt

### December 2, 2008

### 3:00 PM

### AP&M 6402

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