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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2512.03246 |
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| _version_ | 1866917459864322048 |
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| author | Pan, Anping |
| author_facet | Pan, Anping |
| contents | In this paper, we study the inhomogeneous incompressible Euler equation (IIE in short) from a Lagrangian perspective. We establish a geodesic description of this equation and discuss the associated geometric structures. We also find the derivation of IIE from the Hamilton-Pontryagin action principle and derive the corresponding Lagrangian formulation. A byproduct is a new vorticity formulation of IIE. We also prove the Lagrangian analyticity of IIE using our Lagrangian representation formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03246 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Lagrangian Approach to the Inhomogeneous Incompressible Euler Equation Pan, Anping Analysis of PDEs 35A20, 35B38, 58E30, 76B03, 76M30 In this paper, we study the inhomogeneous incompressible Euler equation (IIE in short) from a Lagrangian perspective. We establish a geodesic description of this equation and discuss the associated geometric structures. We also find the derivation of IIE from the Hamilton-Pontryagin action principle and derive the corresponding Lagrangian formulation. A byproduct is a new vorticity formulation of IIE. We also prove the Lagrangian analyticity of IIE using our Lagrangian representation formula. |
| title | A Lagrangian Approach to the Inhomogeneous Incompressible Euler Equation |
| topic | Analysis of PDEs 35A20, 35B38, 58E30, 76B03, 76M30 |
| url | https://arxiv.org/abs/2512.03246 |