中科院数学与系统科学研究院
数学研究所
学术报告
调和分析和偏微分方程研讨班
报告人：Chengyang Shao (The University of Chicago)
题 目：Advances in the Spherical Capillary Water Waves Equation
时 间：2024.01.03（星期三）16:00-17:00
地 点：思源楼S615
摘 要：The speaker aims to report some advances in the study of irrotational oscillation of a water droplet under zero gravity. The governing physical laws, resembling the well-studied capillary water waves equation, are converted to a quasilinear dispersive para-differential system defined on the 2-sphere. Regarding this conversion, a coordinate-independent, global para-differential calculus defined on compact Lie groups and homogeneous spaces is developed as a toolbox. After discussing Cauchy theory under this novel formalism, the speaker will propose several unsolved problems concerning existence of periodic solutions, normal form reduction and generic lifespan estimates. It is pointed out that all of these problems are closely related to certain Diophantine equations.
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