Dispersive properties of surface water waves
- CDSNS Colloquium
- Monday, April 6, 2009 - 16:30 for 2 hours
- Skiles 255
- Vera Mikyoung Hur – MIT
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 open questions regarding long-time behavior and stability.