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Title: A New Blow-up Criterion for the 3D Euler Equations: A Computational Study

Abstract: In this talk we will report the results of a computational investigation of a new blow-up criterion for the 3D incompressible Euler equations, which does not rely on the seminal Beale-Kato-Majda blow-up criterion.

This criterion is 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-Voigt equations. The new criterion is 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.

Notably, the Voigt inviscid regularization approach applies equally to other hydrodynamical models, and it can be shown that its solutions converge, as the regularization parameter goes to 0, to the corresponding solutions of the underlying  hydrodynamical model for as long as the latter exist.

Science Learning Center (SLC), 1.102
800 W. Campbell Road, Richardson, Texas 75080-3021

Natural Sciences & Mathematics


Viswanath Ramakrishna

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