| Abstract: |
| In this talk, we mainly investigate the properties of vertical velocity v for two dimensional
steady water waves over a flat bed. Firstly we prove the existence of the inflection point for each streamline, then we find that the behavior of v along each streamline depends strictly on concavity and convexity of streamline, and prove Constantin`s conjecture on v in Stokes wave. Finally the location of maximum vertical fluid velocity is also proven to be at the inflection point. Furthermore, we also extend our results to the case with vorticity. |
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