The helicity distribution for the 3D incompressible Euler equations

2024/10/03 by Marco Inversi, Massimo Sorella, Inversi, Marco +1 · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · #35D30 #35Q31 #35Q35 #76M15 #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2410.02728

openalex publication_date 2024/10/03 · openalex created_date 2024/10/30 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the helicity associated to solutions of the 3D incompressible Euler equations. We show that under mild conditions on the regularity of the velocity field of an incompressible ideal fluid it is possible to define a defect distribution describing the local helicity balance. Under suitable regularity assumptions, we also provide the global helicity balance on bounded domains in terms of the boundary contributions of the vorticity, velocity and pressure.

Cited by

• A note on helicity conservation for compressible Euler equations in a bounded domain with vacuum

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