云南大学数学与统计学院

线上学术报告-----邬似珏教授（密歇根大学）

报告题目：The quartic integrability and long-time existence of steep water waves in 2D

报告人：邬似珏教授（美国，密歇根大学）Sijue Wu (University of Michigan, US)

报告时间：2021年10月14日星期四上午9：00—10：00

Zoom会议号：815 6088 3195

密码：244524

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https://zoom.us/j/81560883195?pwd=anljemJnVmJBUVUvemFaQUxqT29tUT09

报告摘要：It is known since the work of Dyachenko \& Zakharov in 1994 that for the weakly nonlinear 2d infinite depth water waves, there are no 3-wave interactions and all of the 4-wave interaction coefficients vanish on the non-trivial resonant manifold. In this talk I will present a recent result that proves this partial integrability from a different angle. We construct a sequence of energy functionals $\mathfrak E_j(t)$, directly in the physical space, which are explicit in the Riemann mapping variable and involve material derivatives of order $j$ of the solutions for the 2d water wave equation, so that $\frac d{dt} \mathfrak E_j(t)$ is quintic or higher order. We show that if some scaling invariant norm, and a norm involving one spacial derivative above the scaling of the initial data are of size no more than $\varepsilon$, then the lifespan of the solution for the 2d water wave equation is at least of order $O(\varepsilon^{-3})$, and the solution remains as regular as the initial data during this time. If only the scaling invariant norm of the data is of size $\varepsilon$, then the lifespan of the solution is at least of order $O(\varepsilon^{-5/2})$. Our long time existence results do not impose size restrictions on the slope of the initial interface and the magnitude of the initial velocity, they allow the interface to have arbitrary large steepnesses and initial velocities to have arbitrary large magnitudes.

个人简介：

邬似珏(Sijue Wu)教授现任美国密歇根大学（University of Michigan）数学系Browne教授，于1990年获美国耶鲁大学博士学位。毕业后，先后在美国纽约大学、西北大学、普林斯顿高等研究院、马里兰大学、密歇根大学工作。

邬似珏教授的专业方向是调和分析和偏微分方程，她是水波方程(water waves problem)领域的资深专家，在水波问题解的适定性相关问题方面做出了一系列突出贡献。邬教授获得过众多荣誉，比如2001年获得美国数学会Satter Prize以及中国晨兴数学银奖， 2002年受邀ICM报告， 2010年获得晨兴数学金奖等等。

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