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: 谢春景 教授 （上海交通大学）
Inviter: 张立群
Language: Chinese
Title: Some classifications for steady incompressible Euler system and their applications
Time & Venue: 2026年4月14日（星期二）14：30-16：30 & 南楼N208
Abstract:When two-dimensional steady flows are away from stagnation which corresponds to the critical points of the stream functions, the associated Euler equations can be locally reduced to a semilinear equation. On the other hand, stagnation of flows is not only an interesting phenomenon in fluid mechanics, but also plays a significant role in understanding many important properties of fluid equations. It also induces many challenging problems in analysis. First, we discuss the scenario when the Euler equations can be reduced to a single semilinear equation in terms of stream function, where the analysis for the topology of critical point sets and the overdetermined elliptic problems plays a crucial role. Second, we give a classification of incompressible Euler flows via the set of flow angles, where a counterpart of Picard's little theorem for steady Euler equations is established. Finally, the selection for the solutions of Euler equations via vanishing viscosity limit will be addressed.
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