具有毛细作用的液滴与旋转行波
偏微分方程分析
2026-03-31 v2
摘要
我们考虑一个三维、不可压缩、无旋、近球形的具有毛细作用的液滴的自由边界问题。我们从基本出发研究该问题，将一些经典结果从平面情形（毛细水波）推广到球面几何：边界上的约化、其哈密顿结构、Sobolev 类中 Dirichlet-Neumann 算子的解析性与 tame 估计，以及利用 Alinhac 的好未知量方法和微分几何方法对其进行的线性化公式。然后我们证明行波的分岔，这些行波是非平凡的（即非球面）固定剖面，以恒定角速度旋转。
引用
@article{arxiv.2408.02333,
title = {Liquid drop with capillarity and rotating traveling waves},
author = {Pietro Baldi and Vesa Julin and Domenico Angelo La Manna},
journal= {arXiv preprint arXiv:2408.02333},
year = {2026}
}
备注
Main changes in version 2: Lemma 4.2 has a new, simpler and shorter proof; Section 5 has a simpler, more classical and much shorter proof, and a slightly weaker result; former Section 7 (Appendix) has been removed. Former Sections 5 and 7 of arXiv:2408.02333v1 have been moved, and improved, into a separate article about the Dirichlet-Neumann operator