PDE Methods in Kinetic Theory and Their Applications

国际和平研究所建议研究以玻尔兹曼理论为中心的动力学模型中出现的数学问题。他计划通过最近开发的数学工具来研究正则性和流体动力学极限问题中的边界效应。PI还建议继续他在天文学中对稳定和不稳定星系模型的研究。PI继续研究Vlasov理论中所谓的BGK波的稳定性。国际和平研究所计划使用新的框架调查流体中“接触线”问题的稳定性。这些研究项目有望开发出新的数学工具。动力学理论和模型在我们理解科学、工程乃至社会科学中的各种问题(如蜂群问题)中发挥着越来越重要的作用。这项建议旨在研究材料科学中研究稳定星系构型、太阳风动力学、聚变中壁-等离子体相互作用的等离子体稳定性控制、薄膜接触线动力学等方面的数学问题。

The PI proposes to study mathematical problems arising in kinetic models centered at the Boltzmann theory. He plans to investigate boundary effects in regularity and hydrodynamic limit problems via recently developed mathematical tools. The PI also proposes to continue his study of stable and unstable galaxy models in astronomy. The PI continues to work on stability of so-called BGK waves in the Vlasov theory. The PI plans to investigate stability of `contact line' problems in fluids using new frameworks. It is expected that new mathematical tools will be developed in these research projects.The kinetic theory and models play an ever increasingly important role in our understanding of various problems in science, engineering and even social science (e.g. swarming). This proposal is set to investigate mathematical problems arising in the study of stable galaxy configurations, dynamics of solar winds, plasma stability control of wall-plasma interaction in fusion, contact line dynamics for thin-film in material sciences.