arXiv subjects

Anping Pan

Publications and source records attributed to Anping Pan.

3 recordsLinked to original sources

arXiv2026

Remarks on Lifespan and Continuation Criteria of Two Dimensional Incompressible Fluid Models

In this paper, we study the lifespan and continuation criteria of several two-dimensional incompressible fluid models. Motivated by a novel energy-vorticity formulation, combining linear transport estimate and a bootstrap argument, we are able to show several longtime existence results of two dimensional fluid models in the close-to-Euler regime. A byproduct of our approach is a new conditional BKM type result for the inhomogeneous incompressible Euler equation.

math.AP↗

arXiv2025

A Lagrangian Approach to the Inhomogeneous Incompressible Euler Equation

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.

math.AP↗

arXiv2025

Variational Principle and Stochastic Lagrangian Formulation of Viscous Hydrodynamic Equations

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.

math.AP↗