Speaker: 李嘉旭，香港中文大学

Inviter: 

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

Language: Chinese 

Time & Venue: 2024.12.16 10:00-11:00 腾讯会议号：393 112 782 密码:80806 

Abstract: 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. This is joint work with Prof. Xin Liu and Dr. Dirk Peschka.