Systematic Search for Singularities in Euler-Voigt flows

Noah Bensler (McMaster)

Monday, March 09, 11:30 (HH403/AIMS Lab)

The question of whether or not the Navier-Stokes equations, or the inviscid Euler equations, are a valid description of fluid mechanics remains unanswered. The Euler-Voigt equations are an inviscid regularization of the Euler equations which are known to be globally well-posed from smooth initial conditions. As the regularization parameter approaches zero, the solutions of Euler-Voigt converge to the solutions of Euler. We examine the Euler-Voigt equations with a PDE-constrained optimization problem to identify smooth initial conditions that produce ’extreme’ behaviour in numerical simulations.  We search for numerical evidence of singularity formation in the Euler equations by repeating this optimization problem as the regularization parameter approaches zero.