On the Cauchy Problem of Spherical Capillary Water Waves
arXiv:2310.07113
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.
Second split from arXiv:2304.10519. arXiv admin note: text overlap with arXiv:2310.06806