2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125080We consider the vorticity formulation of the 2-D viscous Camassa-Holm equations in the whole space. We establish global existence for solutions corresponding to initial data in $L^1$ and describe the large time behavior of solutions with sufficiently small and localized initial data. We calculate the rate at which such solutions approach an ``un-filtered'' Oseen vortex by computing the rate at which the solution of a scaled vorticity problem approaches the solution to a corresponding linearized equation.22 pages, submittedAnalysis of PDEs35B40; 35K55text