3D incompressible Euler: Geometric formalism and a hypothetical self-similar flow

2014/07/18 by Michael Reiterer, Reiterer, Michael
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1407.5047

openalex publication_date 2014/07/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We give a geometric formulation of 3D incompressible Euler that contains the Eulerian and Lagrangian gauges as special cases. In the Lagrangian gauge, incompressible Euler is a real analytic ODE in Banach space; a short proof of this known result is given. We then describe (in a self-contained section) some basic properties of a hypothetical self-similar solution to 3D incompressible Euler.

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