Variational Principle and Stochastic Lagrangian Formulation of Viscous Hydrodynamic Equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912739695263744 |
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| author | Mazzucato, Anna Pan, Anping |
| author_facet | Mazzucato, Anna Pan, Anping |
| contents | In this manuscript, we extend Constantin-Iyer's Lagrangian formulation of Navier-Stokes Equation to a wider class of hydrodynamic models. Moreover, we prove that such Lagrangian formulation is naturally derived from a stochastic Hamilton-Pontryagin type variational principle. Generalized version of Kelvin circulation theorem in viscous fluids is also discussed. We also derive self-contained local well-posedness results of fluid models based on Lagrangian-Eulerian formulation using fixed point argument. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_21498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational Principle and Stochastic Lagrangian Formulation of Viscous Hydrodynamic Equations Mazzucato, Anna Pan, Anping Analysis of PDEs 35C99, 35Q35, 58E30, 60H30, 76D05, 76M30 In this manuscript, we extend Constantin-Iyer's Lagrangian formulation of Navier-Stokes Equation to a wider class of hydrodynamic models. Moreover, we prove that such Lagrangian formulation is naturally derived from a stochastic Hamilton-Pontryagin type variational principle. Generalized version of Kelvin circulation theorem in viscous fluids is also discussed. We also derive self-contained local well-posedness results of fluid models based on Lagrangian-Eulerian formulation using fixed point argument. |
| title | Variational Principle and Stochastic Lagrangian Formulation of Viscous Hydrodynamic Equations |
| topic | Analysis of PDEs 35C99, 35Q35, 58E30, 60H30, 76D05, 76M30 |
| url | https://arxiv.org/abs/2511.21498 |