Speaker: Associate Professor Hou Qianqian
Topic: Global solutions to the free boundary problem of a chemotaxis-Navier-Stokes system
Date: June 28, 2023
Time: 10:00 - 12:00 a.m.
Tencent Meeting ID: 958-794-085
Sponsors: School of Mathematics and Statistics, Research Institute of Mathematical Science, Institute of Science and Technology
Biography：
Hou Qianqian is an associate professor at the Institute for Advanced Studies in Mathematics, Harbin Institute of Technology. She obtained her doctorate in 2018 from the Department of Applied Mathematics of Hong Kong Polytechnic University. Her research mainly focuses on mathematical studies of chemotaxis models, including classical chemotaxis models and well-posedness of solutions for chemotaxis-fluid coupling models. The projects she has led have been supported by the National Natural Science Foundation of China for Young Scholars and China Postdoctoral Special Support Program. She also published papers in journals such as JMPA, SIAM JMA, Nonlinearity and JDE.
Abstract:
Chemotaxis is a common phenomenon in biology. Concerning the liquid living environment of micro-organisms, Tuval et al. proposed a chemotaxis-Navier-Stokes system to describe the dynamics of cell-fluid interactions based on experimental observations. In this talk, we investigate the global solvability of the chemotaxis-Navier-Stokes system on a three-dimensional moving domain of finite depth, bounded below by a rigid flat bottom and bounded above by the free surface. We establish the global existence and uniqueness of solutions near a constant state $(0,\hat{c},0)$, where $\hat{c}$ is the saturation value of the oxygen on the free surface.