Uniqueness of weak solutions for the primitive equations and CAO-system

Establish uniqueness of weak solutions for the primitive equations and for the coupled atmosphere-ocean (CAO) system with nonlinear wind-driven interface conditions.

Background

The paper recalls that Lions, Temam, and Wang established existence of weak solutions for both the primitive equations and the CAO-system. It explicitly states that uniqueness remains unresolved for both systems, independently of the paper’s focus on long-term behavior of globally defined strong solutions.

References

Lions, Temam and Wang proved in their pioneering work the existence of a weak solution to the primitive equations and to the CAO-system ; its uniqueness remains an open problem for both systems until today.

— Long-term behaviour of the CAO-system: Optimal polynomial $H^1$-convergence to degenerate equilibria  (2609.08664 - Binz, 8 Sep 2026) in Section 1, Introduction