PDE Methods in Kinetic Theory and Their Applications

PI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还建议继续研究天文学中的稳定和不稳定星系模型。PI继续研究Vlasov理论中所谓的BGK波的稳定性。PI计划使用新的框架研究流体中“接触线”问题的稳定性。在这些研究项目中，我们可以预见到新的数学工具将被开发出来，动力学理论和模型在我们理解科学、工程甚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。该计划旨在研究稳定星系构型、太阳风动力学、聚变中壁面-等离子体相互作用的等离子体稳定性控制、材料科学中薄膜接触线动力学等研究中出现的数学问题。

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.