报告题目：Shallow water equations with surface tension and contact lines: Derivation, well-posedness, and global stability

报 告 人：李嘉旭（深圳大学）

报告时间：2026年10月29日  10:30-11:30

报告地点：格物楼534（研讨室）

报告摘要：

We consider the one-dimensional shallow water problem with capillary surfaces and moving contact lines. The shallow water equations are derived from the two-dimensional water wave equations in the asymptotic regime where the depth of the water is small. The contact lines are set to have constant contact angles, and become the free boundary at the level of shallow water equations. Moreover, the depth of the shallow water degenerates near the free boundary, which causes singularities for the derivatives due to the loss of uniform parabolicity. We identify a concave and compact equilibrium state of the system, and the global stability of the equilibrium is established in this paper.

报告人简介：

李嘉旭，深圳大学数学科学学院。2021年于中国科学院数学与系统科学研究院获博士学位，2021-2024年在香港中文大学数学科学研究所从事博士后研究。主要从事偏微分方程与流体力学数学理论研究，聚焦Navier-Stokes方程的适定性与稳定性、含真空与退化黏性的流体模型，以及浅水方程与自由边界问题。研究成果发表于Arch. Ration. Mech. Anal.、Calc. Var. Partial Differential Equations、SIAM J. Math. Anal.、J. Differential Equations、Sci. China Math.等国际学术期刊。