2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57647By exploring a local geometric property of the vorticity field along a vortex filament, we establish a sharp relationship between the geometric properties of the vorticity field and the maximum vortex stretching. This new understanding leads to an improved result of the global existence of the 3-D Euler equation under mild assumptions that are consistent with the observations from recent numerical computations.21 pagesMathematical Physics76B03text