报告题目：Global existence and convergence rates to a chemotaxis-fluids system with mixed boundary conditions.

报告人：向昭银教授（电子科技大学）

报告时间：2021年12月05日14：00-16：00

报告地点：数学与统计学院4号楼302室/ID: 645590471

报告摘要：

In this paper, we investigate the large time behavior of strong solutions to a chemotaxis-fluids system in an unbounded domain with mixed boundary conditions. Based on the anisotropic Lp technique, the elliptic estimates and Stokes estimates, we first establish the global existence of strong solution around the equilibrium state (0,csatn,0) with the help of the continuity arguments, where csatn is the saturation value of oxygen inside the fluid. Then we use De Giorgi's technique and energy method to show that such a solution will converge to (0,csatn,0) with an explicit convergence rate in the chemotaxis-free case. Our assumptions and results are consistent with the experimental descriptions and the numerical analysis. The novelty here consists of deriving some new elliptic estimates and Stokes estimates, and choosing a suitable weight in De Giorgi's technique to deal with the mixed boundary conditions

报告人简介：

向昭银，电子科技大学数学科学学院教授、博士生导师、副院长；2006年博士研究生毕业于四川大学；先后访问Johns Hopkins University、北京大学、香港城市大学、香港中文大学、香港理工大学、Imperial College London等；主要从事偏微分方程的研究，在《Communication in Partial Differential Equations》、《Calculus of Variations and Partial Differential Equations》、《International Mathematics Research Notices》、《Journal of Functional Analysis》、《Mathematische Zeitschrift》、《Mathematical Models and Methods in Applied Sciences》、《Journal of Differential Equations》、《Nonlinearity》 等国际著名SCI期刊上发表学术论文 60 余篇；主持国家自然科学基金面上项目、中国博士后科学基金、教育部留学回国人员科研启动基金等；入选四川省杰出青年学术技术带头人资助计划、四川省学术和技术带头人后备人选等。