李玉祥

Global weak solutions and boundedness for 3-D chemotaxis-fluid system with p-Laplacian diffusion  

报告人简介：

李玉祥，教授，博士生导师，东南大学数学学院副院长。研究方向为非线性偏微分方程及其应用；非线性Keller-Segel方程的长时间渐近行为、爆破性态分析；非线性热方程的的长时间渐近行为、爆破性态分析；KPZ界面方程的长时间渐近行为、梯度爆破性态分析。已在CMP，Math Ann，JDE，European J. Appl. Math，DCDS等杂志上发表三十多篇论文。主持国家自然科学基金三项。

报告时间：2018年5月25日下午17:00-18：00    

Abstract: We consider an incompressible chemotaxis-Navier-Stokes system with p-Laplacian diffusion under homogeneous boundary conditions of Neumann type for density of bacteria and concentration of nutrient, and of Dirichlet type for fluid in a bounded convex domain with smooth boundary                                                                                                                                                                                                                                                             . First we prove that if p>32/15 and under appropriate structural assumptions on parameters, for all sufficiently smooth initial data, the model possesses at least one global weak solution. Then we prove that for the incompressible chemotaxis-Stokes system, the global weak solutions is bounded whenever p>25/12.