PDE Methods in Kinetic Theory and Their Applications

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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.