A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization
- Author(s): Larios, A
- Petersen, MR
- Titi, ES
- Wingate, B
- et al.
Published Web Locationhttps://doi.org/10.1007/s00162-017-0434-0
© 2017, Springer-Verlag Berlin Heidelberg. 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 α> 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.