偏微分方程研讨班：Structural Stability of Mixed Riemann Configurations Containing Centered Rarefaction Waves and Surfaces of Discontinuities of Gas Dynamics in Multi-Dimensions

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: 罗涛 教授  (香港城市大学)

Inviter: 郝成春

Language: Chinese

Title: Structural Stability of Mixed Riemann Configurations Containing Centered Rarefaction Waves and Surfaces of Discontinuities of Gas Dynamics in Multi-Dimensions

Time & Venue: 2026年6月8日（星期一）9：00-10：00 &  数学院南楼N913

Abstract: For 2D compressible Euler equations of gas dynamics, we prove the structural stability of mixed Riemann configurations containing centered rarefaction waves and surfaces of discontinuities (such as vortex sheets), by deriving simultaneous energy estimates for acoustic and vorticity waves within the rarefaction wave region and the nonlinear superpositions of rarefaction waves with other waves such as vortex sheets. This is joint work with Prof. Jin Jia of Hunan University.

--------------------------------------------------------

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).