A Computational Investigation of the Finite-Time Blow-Up of the 3D Incompressible Euler Equations Based on the Voigt Regularization
Titi, Edriss S.
Theoretical and Computational Fluid Dynamics
Reason for embargo
This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Springer Verlag
We report the results of a computational investigation of two blowup 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.
The work of E.S.T. was supported in part by ONR grant number N00014-15-1-2333, and by the NSF grants number DMS-1109640 and DMS-1109645.
The 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 This paper had controversial peer review and was withdrawn from PRL and submitted to Theoretical and Computational Fluid Dynamics where it was accepted, but with a weaker statement about the possibility of finite-time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 first draft of this paper is in ORE: http://hdl.handle.net/10871/19090