# Mathematics Colloquia and Seminars

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### Dispersive properties of surface water waves

**Colloquium**

Speaker: | Vera Mikyoung Hur, MIT |

Location: | 1147 MSB |

Start time: | Wed, Jan 7 2009, 4:10PM |

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 precise account of the formulation of the surface water-wave problem and discussion 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.