Published Paper

Inserted: 6 sep 2024
Last Updated: 15 dec 2025

Journal: Archive for Rational Mechanics and Analysis
Volume: 250
Pages: Article number 4
Year: 2026
Doi: https://doi.org/10.1007/s00205-025-02156-2

Abstract:

We consider the free boundary problem for a 3-dimensional, incompressible, irrotational liquid drop of nearly spherical shape with capillarity. We study the problem from scratch, extending some classical results from the flat case (capillary water waves) to the spherical geometry: the reduction to a problem on the boundary, its Hamiltonian structure, the analyticity and tame estimates for the Dirichlet-Neumann operator in Sobolev class, and a linearization formula for it, both with the method of the good unknown of Alinhac and by a differential geometry approach. Then we prove the bifurcation of traveling waves, which are nontrivial (i.e., nonspherical) fixed profiles rotating with constant angular velocity.