报告题目：Classification of finite-time blow-up of strong solutions to the incompressible free boundary Euler equations with surface tension

报告人：罗涛 教授 Tao Luo (City University of Hong Kong)

报告时间：2025年9月24日星期三下午15：30—16：30

腾讯会议号：421-714-000

会议密码：0924

https://meeting.tencent.com/dm/hIaiaeOa7jmU

报告摘要：In this talk, I will discuss the complete classification of finite-time blow-up scenarios for strong solutions to the three-dimensional incompressible Euler equations with surface tension in a bounded domain possessing a closed, moving free boundary.  We make \textit{no} assumptions on symmetry, periodicity, graph representation, or domain topology (simple connectivity). At the maximal existence time $T<\infty$, up to which the velocity field and the free boundary can be continued in $H^3\times H^4$,  blow-up must occur in at least one of five mutually exclusive ways: (i) self-intersection of the free boundary for the first time; (ii) loss of mean curvature regularity in $H^{\frac{3}{2}}$, or the free boundary regularity in $H^{2+\varepsilon}$ (for any sufficiently small constant $\varepsilon>0$); (iii) loss of $H^{\frac{5}{2}}$ regularity for the normal boundary velocity; (iv) the $L^1_tL^\infty$-blow-up of the tangential velocity gradient on the boundary; or (v) the $L^1_tL^\infty$‐blow-up of the full velocity gradient in the interior. Furthermore, for simply connected domains, blow-up scenario (v) simplifies to a vorticity-based Beale-Kato-Majda criterion, and in particular, irrotational flows admit blow-up only at the free boundary.  This talk is based on the joint work with Prof. Chengchun Hao at Chinese Academy of Sciences and Prof. Siqi Yang at Beijing University of Technology.

个人简介：罗涛教授1995年在中国科学院数学与科学研究院获得博士学位，现就职于香港城市大学数学系。曾经任职于密歇根大学安娜堡分校，乔治城大学和伍斯特理工学院。罗涛教授的研究方向和学术兴趣包括可压Navier-Stokes方程组，Euler-Poisson方程，可压Euler方程等，已在Comm. Pure Appl. Math.，SIAM J. Math. Anal. ，Arch. Ration. Mech. Anal.， Proc. Roy. Soc. Edinburgh， Comm. Math. Phys. ，Ann. Inst. H. Poincaré Anal. Non Linéaire等多种国际著名学术期刊上发表过许多研究成果。

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