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- Title
A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization.
- Authors
Larios, Adam; Petersen, Mark; Titi, Edriss; Wingate, Beth
- Abstract
We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for fixed values of the regularization parameter $$\alpha >0$$ . Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly, namely by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be sufficient criterion for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well known to occur.
- Subjects
EULER equations; VOIGT reaction; INVISCID flow; MATHEMATICAL models of turbulence; BURGERS' equation
- Publication
Theoretical & Computational Fluid Dynamics, 2018, Vol 32, Issue 1, p23
- ISSN
0935-4964
- Publication type
Article
- DOI
10.1007/s00162-017-0434-0