Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability

TL;DR

This paper establishes a variational principle for stochastic Lagrangian Navier-Stokes trajectories on manifolds, analyzing their stability and particle rotation, with detailed focus on the two-dimensional torus case.

Contribution

It introduces a variational framework for stochastic Navier-Stokes trajectories on manifolds, advancing understanding of their stability and rotational behavior.

Findings

Proves a variational principle for stochastic Lagrangian Navier-Stokes on manifolds.

Analyzes stability and particle rotation of trajectories.

Provides detailed analysis for the two-dimensional torus case.

Abstract

We prove a variational principle for stochastic Lagrangian Navier-Stokes trajectories on manifolds. We study the behaviour of such trajectories concerning stability as well as rotation between particles; the two-dimensional torus case is described in detail.