Global existence for general vorticity configurations

Establish global existence for two-dimensional gravity water-wave systems with general nontrivial vorticity configurations, beyond the finite point-vortex setting considered in the paper.

Background

The paper contrasts the well-developed global theory for irrotational two-dimensional gravity water waves with the substantially less understood rotational case, in which the vorticity is transported by the fluid and can develop filamentary small-scale structures. The authors prove global well-posedness only for a specific configuration consisting of two point vortices of opposite strengths that retreat from the free surface. They explicitly identify global existence for general vorticity configurations as an unresolved problem because the interaction between transported interior vorticity and the dispersive free-boundary dynamics remains difficult to control.