中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
偏微分方程研讨班
Speaker: 杨思奇 讲师 (北京工业大学)
Inviter: 郝成春
Language: Chinese
Title: Blow-up and boundary singularity formation in free boundary incompressible ideal fluids
Time & Venue: 2026年6月8日（星期一） 10：00-11：00 & 数学院南楼N913
Abstract: This talk explores finite-time blow-up classification and boundary singularity formation in the free boundary problems (FBPs) of incompressible Euler and ideal magnetohydrodynamic (MHD) equations with surface tension. We first present the a priori estimates and a blow-up criterion for the FBP of the MHD equations in general bounded domains without the simply-connected or graph assumptions. Building on this, we provide a complete finite-time blow-up classification of low-regularity solutions to the FBP of the Euler equations, identifying scenarios such as boundary self-intersection and curvature blow-up. Specifically, when the fluid domain is simply connected, the interior blow-up criterion is refined into a vorticity-dependent Beale-Kato-Majda type criterion. Finally, we briefly outline the construction of the boundary self-intersecting singular solutions anticipated in our blow-up classification. This talk is based on joint work with Prof. Chengchun Hao (AMSS) and Prof. Tao Luo (CityUHK).
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