Variational Principle and Stochastic Lagrangian Formulation of Viscous Hydrodynamic Equations

Anna Mazzucato; Anping Pan

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arXiv · 2511.21498

Variational Principle and Stochastic Lagrangian Formulation of Viscous Hydrodynamic Equations

Anna Mazzucato·Anping Pan

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Abstract

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.

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Anna Mazzucato, Anping Pan. 2025-11-26. Variational Principle and Stochastic Lagrangian Formulation of Viscous Hydrodynamic Equations. https://arxiv.org/abs/2511.21498

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