报告题目：Analysis of the singularity set of the 3D chemotaxis-Navier-Stokes equations

报告人： 王文栋 教授(大连理工大学)

报告时间：2023年12月29日上午10点00 分-11点30分

报告地点： 腾讯会议：964-517-281

报告摘要：In 2004, Dombrowski et al. observed that Bacterial flow in a sessile drop related to those in the Boycott effect of sedimentation can carry bioconvective plumes, and the horizontal ``turbulence'' white line near the top is the air-water-plastic contact line. In pendant drops such self-concentration occurs at the bottom. On scales much larger than a cell, concentrated regions exhibit transient, reconstituting, high-speed jets straddled by vortex streets. We investigate the Hausdorff dimension of these vortices (singular points) by considering partial regularity of weak solutions of the three dimensional chemotaxis-Navier-Stokes equations, and showed that the singular dimension is not larger than $1$, which seems to be consistent with the linear singularity in the experiment.

报告人简介：王文栋，大连理工大学数学科学学院教授、博士生导师。入选国家高层次人才计划青年项目与大连市高层次人才项目，已主持国家自然科学基金四项。博士毕业于中科院数学与系统科学研究院，曾在北京大学、香港中文大学、牛津大学从事博士后研究或担任访问学者。目前研究主要集中在非线性偏微分方程领域，特别是不可压流体方程的数学理论方面（包括Navier-Stokes方程、MHD方程、边界层、趋化模型、液晶方程等）的正则性、稳定性与奇性分析。发表学术论文三十余篇，部分发表在《 Arch. Ration. Mech. Anal.》，《 J. Funct. Anal.》，《Ann. Inst. H. Poincaré C Anal. Non Linéaire》，《Calc. Var. Partial Differential Equations》，《SIAM J. Math. Anal》等。