标题： 泰勒锥的狄利克雷-诺伊曼算子 显示英文标题

标题： The Dirichlet-Neumann Operator for Taylor's Cone

摘要： 本文的目的是分析轴对称圆锥域中的Dirichlet-Neumann算子。 我们通过使用一种新的坐标系来构造性地处理顶点处的通用奇异性，该坐标系将圆锥域映射到一个条带。 在拟微分理论的基础上，我们建立了主要的Sobolev估计。 我们还找到了Dirichlet-Neumann算子的形状导数、线性化公式和抵消性质。 我们的结果可以被视为建立Taylor锥扰动数学框架的第一步，该框架出现在喷流断裂控制中。 显示英文摘要

摘要： The aim of this paper is to analyse the Dirichlet-Neumann operator in axially symmetric conical domains. We provide a constructive treatment of the generic singularity at the vertex by using a new coordinate system that maps the conical domain to a strip. Building upon the paradifferential theory, we then establish our main Sobolev estimates. We also find the shape derivative, the linearization formula, and the cancellation property for the Dirichlet-Neumann operator. Our results can be viewed as the first step towards establishing the mathematical framework for the perturbations of Taylor's cone which appears in the jet break-up control.