On the Cauchy Problem of Spherical Capillary Water Waves
Analysis of PDEs
2023-10-12 v1
Abstract
The spherical capillary water waves equation describes the motion of an almost spherical water droplet under zero gravity governed by water-air interface tension. Using para-differential calculus on compact Lie groups and homogeneous spaces developed by the author, the system is symmetrized into a quasi-linear dispersive para-differential equation of order 1.5 defined on the 2-sphere. An immediate consequence of this symmetrization is a new proof of local well-posedness of the system under much weaker regularity assumption compared to previous results.
Keywords
Cite
@article{arxiv.2310.07113,
title = {On the Cauchy Problem of Spherical Capillary Water Waves},
author = {Chengyang Shao},
journal= {arXiv preprint arXiv:2310.07113},
year = {2023}
}
Comments
Second split from arXiv:2304.10519. arXiv admin note: text overlap with arXiv:2310.06806