Uniqueness for two-dimensional Euler solutions with finite-p integrable vorticity

Prove uniqueness for unforced two-dimensional Euler solutions whose vorticity belongs to L^p for finite p<\infty.

Background

The paper contrasts Yudovich’s uniqueness theorem for bounded vorticity with the unresolved uniqueness problem below the bounded-vorticity threshold. The question concerns unforced two-dimensional Euler solutions with vorticity in Lp for finite p, without assuming L\infty control.

References

Yudovich's theorem gives global well-posedness for bounded vorticity, while uniqueness for unforced solutions with vorticity merely in Lp, p<\infty, remains open.

— Flexibility for the Three-Dimensional Navier-Stokes Equations via Moving Hill Vortices  (2608.20068 - Nguyen et al., 20 Aug 2026) in Section 1, subsection “Background and related work”