Speaker: 杨思奇讲师，北京工业大学

Inviter: 郝成春

Title: Blow-up and boundary singularity formation in free boundary incompressible ideal fluids

Language: Chinese

Time & Venue: 2026.06.08 10:00-11:00 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).