A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization
Titi, Edriss S.
Physical Review Letters
American Physical Society
We report the results of a computational investigation of two recently proved blow-up criteria for the 3D incompressible Euler equations. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations. The latter 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 criteria 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.
Submitted to Physical Review Letters
This first draft of this paper, submitted to Physical Review Letters, made a strong statement about the possibility of finite-time blow up in the Euler Equations. This paper had controversial peer review and was withdrawn from PRL and submitted to Theoretical and Computational Fluid Dynamics where it was accepted, but with a weaker statement about the possibility of finite-time blow up in the Euler-Equations.
The accepted version of this paper - accepted for publication in 2017 in Theoretical and Computational Fluid Dynamics - is in ORE at http://hdl.handle.net/10871/27195
Published online 29 April 2017
- Mathematics