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Toolbox of Para-differential Calculus on Compact Lie Groups

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arxiv 2310.06806 v1 pith:RTAYI6S5 submitted 2023-10-10 math.AP

Chengyang Shao This is my paper · ORCID
classification math.AP
keywords calculustoolboxcompactgroupspara-differentialoperatorssymboliccertain
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This paper provides a toolbox of para-differential calculus on compact Lie groups. The toolbox is based on representation theory of compact Lie groups and contains exact formulas of symbolic calculus. Para-differential operators are constructed in a global, coordinate-free manner, giving lower order terms in symbolic calculus a clear form. The toolbox helps to understand non-local, nonlinear differential operators defined on certain manifolds with high symmetry.

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  1. Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions

    math.AP 2025-06 conditional novelty 6.0 of 10

    For the 2D free-boundary Euler equations with surface tension on a droplet, there exist arbitrarily small initial velocities such that the vorticity Hessian grows at least exponentially in time.

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