Dissipative Euler flows originating from circular vortex filaments

2024/04/05 by Francisco Gancedo, Gancedo, Francisco, Antonio Hidalgo-Torné +3 · 1 citation
Engineering · Mathematics · #76B03 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Plasma and Flow Control in Aerodynamics

paper · pdf · doi:10.48550/arxiv.2404.04250

openalex publication_date 2024/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the first existence result of weak solutions to the 3D Euler equation with initial vorticity concentrated in a circle and velocity field in C([0,T],L^2-). The energy becomes finite and decreasing for positive times, with vorticity concentrated in a ring that thickens and moves in the direction of the symmetry axis. With our approach, there is no need to mollify the initial data or to rescale the time variable. We overcome the singularity of the initial data by applying convex integration within the appropriate time-weighted space.

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