Renormalization and blow-up for the 3D Euler equations

Abstract

In recent work we have developed a renormalization framework for stabilizing reduced order models for time-dependent partial differential equations. We have applied this framework to the open problem of finite-time singularity formation (blow-up) for the 3D Euler equations of incompressible fluid flow. The renormalized coefficients in the reduced order models decay algebraically with time and resolution. Our results for the behavior of the solutions are consistent with the formation of a finite-time singularity.

References in corpus (6)

• Potentially Singular Solutions of the 3D Incompressible Euler Equations
• Data-driven parameterization of the generalized Langevin equation
• Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations
• Application of the t-model of optimal prediction to the estimation of the rate of decay of solutions of the Euler equations in two and three dimensions
• Interplay between the Beale-Kato-Majda theorem and the analyticity-strip method to investigate numerically the incompressible Euler singularity problem
• Finite-time Singularity formation for Strong Solutions to the axi-symmetric $3D$ Euler Equations