2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145988This paper deals with the global well-posedness of the 3D axisymmetric Euler equations for initial data lying in critical Besov spaces $B_{p,1}^{1+3/p}$. In this case the BKM criterion is not known to be valid and to circumvent this difficulty we use a new decomposition of the vorticity.28 pages. This is an updated version of the paper (arXiv:math/0703144). The main result is improvedAnalysis of PDEs76D03 (35B33 35Q35 76D05)text