Renormalization and blow-up for the 3D Euler equations
This work addresses the open problem of blow-up in the 3D Euler equations, providing computational evidence for singularity formation.
The authors developed a renormalization framework for reduced order models of time-dependent PDEs and applied it to the 3D Euler equations, finding evidence consistent with finite-time singularity formation via algebraic decay of coefficients.
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.