The Dirichlet-Neumann Operator for Taylor's Cone
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909101870546944 |
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| author | Huang, Yucong Karakhanyan, Aram |
| author_facet | Huang, Yucong Karakhanyan, Aram |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Dirichlet-Neumann Operator for Taylor's Cone Huang, Yucong Karakhanyan, Aram Analysis of PDEs Mathematical Physics Functional Analysis 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. |
| title | The Dirichlet-Neumann Operator for Taylor's Cone |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2402.07005 |