主讲人简介：

Michael Winkler现为德国帕德博恩大学教授，是抛物偏微分方程，尤其是趋向性模型研究领域的国际知名专家。现担任4份SCI国际期刊M3AS, JMAA, DCDS-B, NAwra编委，已在ARMA, CPDE, POINCARE, JDE等著名数学期刊上发表了100篇论文。

报告摘要：

We consider models for the spatio-temporal evolution of populations of microorganisms, moving in an incompressible fluid, which are able to partially orient their motion along gradients of a chemical signal.

According to modeling approaches accounting for the mutual interaction of the swimming cells and the surrounding fluid, we study parabolic chemotaxis systems coupled to the (Navier-)Stokes equations through transport and buoyancy-induced forces.

The presentation discusses mathematical challenges encountered even in the context of basic issues such as questions concerning global existence and boundedness, and attempts to illustrate this by reviewing some recent developments. A particular focus will be on strategies toward achieving a priori estimates which provide information sufficient not only for the construction of solutions, but also for some qualitative analysis.