| Abstract: |
| We consider the two-dimensional water wave equation which is a model of ocean waves. In the case of zero surface tension, we show that the angled crested solutions constructed by Wu are rigid, in the sense that the angle of the crest does not change nor does it tilt and the tip is in free fall. In the case of non-zero surface tension, we construct smooth solutions which approximate the sharp crested solutions and prove that in an appropriate scaling regime, the zero surface tension limit of our solutions are waves with angled crests. |
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