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资源 63
[Lecture] Advances in Spherical Capillary Water Waves Equation
Jan. 24, 2024
Speaker: Shao Chengyang, The University of Chicago

Time: 14:00-15:00 p.m., January 24, 2024, GMT+8

Venue: Siyuan Hall, Zhihua Building, PKU


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 problems concerning existence of periodic solutions, normal form reduction and generic lifespan estimates. It is pointed out that  these problems are closely related to certain Diophantine equations.

Source: School of Mathematical Sciences, PKU