A Blow-Up Criterion for the 3D Euler Equations Via the Euler-Voigt Inviscid Regularization

TL;DR

This paper introduces a new blow-up criterion for the 3D Euler equations using the Euler-Voigt regularization, which is computationally more feasible and stronger than previous criteria, aiding in the analysis of fluid flow singularities.

Contribution

The paper develops a novel, stronger blow-up criterion based on the Euler-Voigt regularization, simplifying computational testing for singularities in 3D Euler flows.

Findings

The Euler-Voigt equations are globally well-posed.

The new criterion is more effective for computational tests.

Simulation of Euler-Voigt suffices to test blow-up in Euler equations.

Abstract

We propose a new blow-up criterion for the 3D Euler equations of incompressible fluid flows, based on the 3D Euler-Voigt inviscid regularization. This criterion is similar in character to a criterion proposed in a previous work by the authors, but it is stronger, and better adapted for computational tests. The 3D Euler-Voigt equations enjoy global well-posedness, and moreover are more tractable to simulate than the 3D Euler equations. A major advantage of these new criteria is that one only needs to simulate the 3D Euler-Voigt, and not the 3D Euler equations, to test the blow-up criteria, for the 3D Euler equations, computationally.