主讲人简介：Professor Michael Winkler, from University of Paderborn (Germany), is an expert in nonlinearparabolic Partial Differential Equations, and he has published 112 researchpapers with over 1800 citations.

内容摘要：A class of chemotaxis-Stokes systems with nonlinear self-diffusion in the form of $n^{m-1}$ is considered in bounded convex three-dimensional domains. The goal of the presentation is to describe an analytical approach which consists in a combination of energy-based arguments and maximal Sobolev regularity theory, and which allows for the construction of global bounded weak solutions to an associated initial-boundary value problem under the assumption that $$m>\frac{9}{8} .$$(\star). Moreover, the obtained solutions are shown to approach the spatially homogeneous steady state $(\frac{1}{|\Omega|} \io n_0,0,0)$ in the large time limit. This extends previous results which either relied on different and apparently less significant energy-type structures, or on completely alternative approaches, and thereby exclusively achieved comparable results under hypotheses stronger than (\star).

讲座语言：English