【学术报告】Helical Kelvin Waves for the 3D Incompressible Euler Equations

报告人：曹道民（中国科学院数学与系统科学研究院）

时 间：2025年11月27日15:30

地 点：海韵园实验楼S102

内容摘要:

M-fold symmetric vortex patch solutions form a particularly important class of vortex solutions for the incompressible Euler equations. In the two-dimensional case, numerous results exist. For example, the characteristic function of a disk centered at the origin represents a trivial vortex patch solution. Another well-known example is the Kirchhoff vortex patch, which corresponds to the characteristic function of an elliptical domain. For the three-dimensional incompressible Euler equations, however, while several results have been established for solutions with vorticity highly concentrated along helically symmetric curves (featuring small cross-sections), helical symmetric solutions with large cross-sections remain scarce. This talk presents joint work in which the Crandall–Rabinowitz bifurcation theorem is applied to prove the existence of m-fold symmetric helical vortex patch solutions (also known as m-fold Kelvin waves), whose cross-sections approximate disks. This talk is based on joint work with Boquan Fan, Rui Li, and Guolin Qin.

个人简介：

曹道民，中国科学院数学与系统科学研究院研究员，博士生导师，国家杰出青年科学基金获得者。先后获得中国科学院“青年科学家奖”、“杰出青年”、“优秀导师奖”等荣誉。担任《应用数学学报》和《数学物理学报》副主编以及《Applicable Anal.》、《Ann. Acad. Sci. Fenn. Math.》等学术刊物的编委。主要从事非线性偏微分方程和非线性分析的研究。在《Adv. Math.》，《Arch. Rational Mech. Anal.》，《Comm. PDEs》，《Duke Math. J.》，《Math. Ann.》等国际知名期刊上发表论文160余篇，与人合作在Cambridge University Press出版专著一部。

联系人：詹伟城