GRK 1529: Mathematical Fluid Dynamics

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In modern mathematical fluid dynamics topics as rotational effects, vorticity behaviour, boundary layers and free boundary value problems of Newtonian or more generally Non-Newtonian fluids play a dominant role. The rigorous mathematical treatment of the underlying structures requires novel concepts and methods from various disciplines in mathematics ranging from variational concepts on certain Lie groups, Kolmogorov operators, martingale solutions, optimal control and statistical analysis of Gaussian fields up to rotating boundary layers, free boundary value problems and fluid-solid interactions. The interdisciplinary and international Research Training Group has the aim to examine the mathematical structures of the underlying equations and to apply the results to models from wetting processes as well as to turbulence models. Major contributions to the problems described above are due to the principal investigators at University of Tokyo, Waseda University and TU Darmstadt. Students with a thorough background in at least one of the fields of analysis, stochastics, geometry or optimisation will receive an interdisciplinary education in key areas of mathematical fluid dynamics, enabling them to successfully pursue research on often interdisciplinary problems, which without our common study programme and without the cooperation with our Japanese partners would be much more difficult or even impossible to handle. The yearlong interdisciplinary course and later on the special courses and seminars taught jointly by our German-Japanese team will provide students with one common scientific language in fluid dynamics. This broad but nevertheless focussed education is needed to successfully treat our interdisciplinary projects. Students from Darmstadt are requested to spend at least six months in Tokyo. Due to this international component, the scientific visibility of the PhDs will certainly be a high one.