Convex integration solutions to the incompressible Euler equations with Onsager-critical regularity

What the research examines

By constructing multi-scale high-frequency Beltrami flows with sharp Reynolds stress error cancellation, mathematicians produce non-conservative weak solutions to the 3D incompressible Euler equations possessing exactly Holder-1/3 regularity.

Why it may matter

Provides the definitive mathematical realization of Kolmogorov's anomalous energy dissipation in hydrodynamic turbulence.

What to examine carefully

Solutions constructed via convex integration are highly non-unique and do not represent deterministic Cauchy initial-value solutions.

Try a small, reproducible follow-up

Trace energy dissipation in a 1D shell model of turbulence and verify how Holder 1/3 velocity scaling leads to non-zero kinetic energy dissipation.

Questions to investigate

1. How was the quadratic convective non-linear term balanced against high-frequency oscillation errors?
2. What structural properties distinguish these dissipative solutions from smooth physically realized fluid trajectories?

These are independently proposed educational investigations, not activities that the original research authors claim to have completed.

Publication & researcher information

Multi-author research may involve universities in several countries. Unverified institutions and contact addresses are not inferred from authors' names.

Primary sources