GRK 1529: Mathematical Fluid Dynamics

在现代数学流体动力学中，牛顿或更普遍的非牛顿流体的旋转效应、涡度行为、边界层和自由边值问题等主题起着主导作用。对底层结构的严格数学处理需要来自不同数学学科的新概念和方法，从某些李群的变分概念、Kolmogorov算子、鞅解、高斯场的最优控制和统计分析到旋转边界层、自由边值问题和流固相互作用。跨学科和国际研究培训小组的目标是检查基础方程的数学结构，并将结果应用于从润湿过程的模型以及湍流模型。对上述问题的主要贡献要归功于东京大学、早稻田大学和达姆施塔特工业大学的主要研究人员。在分析、随机、几何或优化领域中至少有一个领域的全面背景的学生将接受数学流体动力学关键领域的跨学科教育，使他们能够成功地进行跨学科问题的研究，如果没有我们共同的学习计划和与日本合作伙伴的合作，这些问题将更加困难，甚至不可能处理。为期一年的跨学科课程以及之后由我们的德日团队联合教授的特别课程和研讨会将为学生提供流体动力学的一种共同科学语言。要成功地处理我们的跨学科项目，这种广泛但重点突出的教育是必要的。来自达姆施塔特的学生被要求在东京至少呆六个月。由于这一国际组成部分，博士们的科学知名度肯定会很高。

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.