报告人：向昭银 教授（成都电子科技大学）

报告题目：Global Existence to a Chemotaxis-Navier-Stokes System with Mixed Boundary Condition

报告时间：2018年8月11日下午16:30-17:30

报告地点：数理大楼661

报告摘要：In this talk, we investigate the large time behavior of strong solutions to a chemotaxis-Navier-Stokes system in an unbounded domain with finite depth and mixed boundary conditions. Based on some uniform a priori estimates obtained by using the anisotropic $L^p$ technique and the subtle elliptic estimates, we first establish the global existence of strong solution around the equilibrium state $(0,c_{\mathrm{air}}, {\bf 0})$  with the help of the continuity arguments, where  $c_{\mathrm{air}}$ is the saturation value of oxygen inside the fluid. Then we use De Giorgi's technique and cutoff method to  show that such a solution will converge to $(0,c_{\mathrm{air}}, {\bf 0})$  with an explicit convergence rate in the chemotaxis-free case. Our assumptions and results are consistent with the experimental  descriptions and the numerical analysis. This is a joint work with Yingping Peng.

联系人：张剑文教授