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Examining Blow-up of the 3D Euler Equations via Inviscid Regularization: A New Computational Approach

Banff International Research Station for Mathematical Innovation and Discovery

We will discuss a computational study of a new blow-up criterion for the 3D incompressible Euler equations, based on the 3D Euler-Voigt equations. Traditional computational searches for blow-up have looked to the enstrophy coming from the 3D Euler equations themselves, which are not known to be globally well-posed, and moreover, are extremely difficult to simulate accurately. In contrast, the new blow-up criterion we investigate relies only on analyzing the enstrophy of the 3D Euler-Voigt equations, which are known to be globally well-posed and are less computationally intensive to simulate accurately over a certain range of the regularization parameter. We also study an analogue of this approach in the setting of the well-understood Burgers equation.

Mathematics; Fluid mechanics; Partial differential equations

video/mp4

Author affiliation: University of California Irvine

2017-01-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59904

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/