Zu Chongzhi Research Seminar

Date and Time (China standard time): Wednesday, May 13, 10:30 – 11:30 am

Location: WDR 1007

Zoom: 986 8782 7545, Passcode: dkumath

Title: A Geophysical Free-Boundary Model for Ice-Ocean Interaction

Speaker: Qi Xu, University of Southern California

Abstract: We consider a free-boundary fluid-structure interaction model for an ocean flow coupled to an elastic ice sheet. The fluid is described by the viscous primitive equations, while the moving upper interface evolves according to an Euler-Bernoulli type equation driven by the fluid pressure. After introducing the model and its relation to free-boundary primitive equations and fluid-structure interaction, I will discuss the ALE reformulation on a fixed reference domain.

The main goal is to establish local-in-time a priori estimates for smooth solutions. The analysis is complicated by the anisotropic structure of the primitive equations, high-order vertical derivatives generated by the ALE coefficients, and pressure terms on the interface. I will explain how anisotropic interpolation, recovery of normal derivatives from the momentum equation, vertical averaging of the pressure equation, and time-differentiated energy estimates are combined to close the argument.

This is joint work with Matthias Hieber, Igor Kukavica, and Amjad Tuffaha.

Bio: Qi Xu is a Ph.D. student in Mathematics at the University of Southern California. His research interests are in the analysis of partial differential equations, fluid dynamics, and fluid–structure interaction.