报告题目：Local Well-posedness for compressible capillary-gravity water waves with acute contact angles

报 告 人：王超 研究员（北京大学）

报告时间：2026年8月28日（星期五）9:30—10:30

报告地点： 数学科学学院111-A      

校内联系人：禹芳 副教授         联系方式：84708351-8504

报告摘要：In this talk, we will talk about the local well-posedness of the compressible Euler equations in a two-dimensional bounded corner domain with acute contact angles. This configuration describes a free surface intersecting the fixed bottom at two points, where the fluid is subject to a gravitational field and the interface between the fluid and air is influenced by capillary forces, without assuming irrotationality. When the contact angles are less than π/2, the local existence theory is established for the solution, with dissipation effects occurring at the contact points. The main analytical challenge arises from the contact points, which renders previous methods for dealing with compressible free boundary problems inadequate. To overcome this, we first establish the geometric structure for the compressible Euler equations, an approach originally introduced by Shatah and Zeng for incompressible fluids. Additionally, we provide a singularity analysis for the wave equations in the corner domain, which ensures the validity of calculations near the corner. Finally, based on the geometric structure and singularity analysis, we obtain a priori energy estimates. Using these estimates, we also prove the local well-posedness of the solutions in a geometric formulation. To our knowledge, this is the first result addressing compressible Euler equations with a free boundary involving contact points.

报告人简介：王超，北京大学数学科学学院研究员、博士生导师，入选国家高层次青年人才计划。博士毕业于中国科学院数学与系统科学研究院，后赴法国巴黎第七大学从事博士后研究。他的研究聚焦流体力学方程中的自由边界问题与粘性极限，主要研究成果发表在CPAM, Memoirs of AMS, ARMA等著名数学期刊。