#Math101 Session 33 (Alumni Talk)

Time：Dec. 25, 2025, 14:00-16:00

Location：E104 Hai Tian Building, Chang'an Campus

Speaker：Mr. Liu, Sizhe (The Chinese University of Hong Kong)

Title：An introduction to inverse problems and relativistic fluid equations with free boundaries

Abstract：This talk provides an introductory overview of two topics in partial differential equations. The first part introduces inverse problems for PDEs, emphasizing the difference between forward and inverse formulations, and discussing basic issues such as uniqueness and stability. In the second part, we present the foundations of relativistic fluid dynamics in flat space-time R^4 equipped with the Minkowski metric. Using the four-velocity and conservation laws, we explain the relativistic Euler equations and show how free boundary problems naturally arise at vacuum interfaces. The aim of the talk is to introduce key concepts and intuition suitable for undergraduate students.