Zu Chongzhi Research Seminar

Date and Time (China standard time): Thursday, April 16, 10:30 – 11:30 am

Location: IB 1051

Zoom: 916 3589 2976, Passcode: dkumath

Title: On a Navier-Stokes-Cahn-Hilliard system with chemotaxis, mass transport, and nonlocal interaction  

Speaker: Hao Wu (Fudan University)

Abstract: We consider a diffuse-interface model for the motion of incompressible viscous two-phase flows with chemotaxis, mass transport, and nonlocal interactions of Oono’s type. The evolution system couples the Navier-Stokes equations for the volume-averaged fluid velocity, a convective Cahn-Hilliard equation for the phase-field variable, and an advection-diffusion equation for the density of a soluble chemical substance. This system can be viewed as a thermodynamically consistent extension of the well-known “Model H” for incompressible binary fluids. For the initial-boundary value problem with a physically relevant singular potential in three dimensions, we report recent results on its well-posedness, propagation of regularity for global weak solutions, and long-time behavior. 

Bio: Hao Wu received his Ph.D. from Fudan University in 2007. Since 2014, he has been a professor at the School of Mathematical Sciences, Fudan University. Hao Wu’s research interests focus on the theoretical study of nonlinear evolution equations, including the well-posedness and long-time behavior of global solutions, as well as associated optimal control problems. He has made progress in the analysis of phase-field models for multi-component systems and hydrodynamic systems of liquid crystal flows. Hao Wu has published over 70 research papers in reputable mathematical journals. He currently serves on the editorial boards of Advances in Differential Equations and Asymptotic Analysis.