Uniqueness and non-uniqueness for the Euler equations with vorticity in Lorentz spaces

What the research examines

This work establishes sharp boundary conditions between deterministic uniqueness and wild non-uniqueness for weak solutions to the 2D Euler equations when vorticity belongs to Lorentz spaces L^{p, q}, settling a conjecture by Yudovich.

Why it may matter

Clarifies fundamental mathematical limits on predictability and deterministic fluid mechanics in singular vortex patches.

What to examine carefully

Non-unique weak solutions are constructed via convex integration and may not be reachable as zero-viscosity limits.

Try a small, reproducible follow-up

Implement the 2D point vortex method in Python and simulate the roll-up of an unstable vortex sheet.

Questions to investigate

1. How is the Biot-Savart singular kernel controlled when vorticity concentration approaches the Lorentz boundary?
2. What explicit initial vorticity profiles lead to branching non-unique weak 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