Time:14:00-15:00, Friday, March 13 2026

Venue: E14-212, Yungu Campus

Speaker: Anping Pan, The Pennsylvania State University

Title: Variational and Lagrangian formulation of Hydrodynamic Equations

Abstract: The seminal work by Arnold and Ebin-Marsden back in 60-70s uncovered the geodesic interpretation of incompressible Euler equation. This geometric framework has since been extensively developed, and the variational nature of inviscid incompressible hydrodynamic models are now well understood. However, existing framework fails to extend to viscous hydrodynamics. Based on Hamilton-Pontryagin action principle in geometric mechanics, we developed a framework to realize many viscous hydrodynamic models as critical points of stochastic action functionals. This variational principle also echoes Constantin-Iyer's stochastic Lagrangian formulation of Navier-Stokes equation. We'll also discuss analysis of local well-posedness, Lifespan estimate and Lagrangian analyticity of fluid PDEs in this Lagrangian framework. This talk is based on joint work with A.Mazzucato.

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