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

2015/07/29 by Adam Larios, Larios, Adam, Edriss S. Titi +1
Engineering · Mathematics · #35A01 #35B44 #35Q30 #35Q31 #35Q35 #76B03 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1507.08203

openalex publication_date 2015/07/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• The three-dimensional Euler equations: Where do we stand?

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