On January 17, 19, 25 and 30, 2024, we held the special lectures “Special Lecture on Mathematical Fluid Dynamics” (100 min. × 8 times) by Professor Dr. Reinhard Josef Farwig (TU Darmstadt). Prof. Farwig is one of the leading mathematicians of mathematical analysis of the Navier-Stokes equations.In addition, he has co-authored 23 papers (published only) with Prof. Hideo Kozono of the Faculty of Science and Engineering, Waseda University.
In this lecture series, Prof. Farwig gave a detailed explanation of his recent research results on moving boundary problems for incompressible viscous flow on unbounded domains, which were obtained through joint works with Prof. Kazuyuki Tsuda (Kyushu Sangyo university). In the moving boundary problems, the shape of the boundary changes along the flow. Therefore, it is necessary to reformulate the system to be considered on a fixed domain. The difficulty arises that the Helmholtz projection, the Stokes operator, and even the gradient operator appearing in the nonlinear terms, which play an essential role in the mathematical study of incompressible fluids, are replaced by time-dependent operators, respectively. The methods of functional analysis were used to derive the mathematical properties of the time-dependent Helmholtz projection and the Stokes operator, and the decay estimate of the associated evolution operator, corresponding to the problem in this lecture series. As an application, he proved the existence of a unique time-periodic solution for small external forces.
For the students of TGU course of Mathematical and Physical Science, it was a great experience to learn the most advanced techniques.
