讲座简介：

In this talk, we investigate the stability of a fully parabolic-parabolic-fluid (PP-fluid) system of the Keller-Segel-Navier-Stokes type in a bounded planar domain under the natural volume filling hypothesis. In the limit of fast signal diffusion, we first show that the global classical solutions of the PP-fluid system will converge to the solution of the corresponding parabolic-elliptic-fluid (PE-fluid) system. As a byproduct, we obtain the global well-posedness of the PE-fluid system for general large initial data. We also establish some new exponential time decay estimates for suitable small initial cell mass, which in particular ensure an improvement of convergence rate on time. To further explore the stability property, we carry out three numerical examples of different types: the nontrivial and trivial equilibriums, and the rotating aggregation. The simulation results illustrate the possibility to achieve the optimal convergence, and show the vanishment of the deviation between the PP-fluid system and PE-fluid system for the equilibriums, and the drastic fluctuation of error for the rotating solution.

讲座人简介：

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 CPDE、CVPDE、IMRN、JFA、Math Z、M3AS、JDE、Nonlinearity 等国际著名SCI期刊上发表学术论文 60 余篇，被菲尔兹奖得主C. Fefferman等数学家引用1000余次；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。