We consider the axisymmetric incompressible Euler equations without swirl in ℝd or in a cylinder domain for d ≥ 3. For 3 ≤ d ≤ 6, we prove the global regularity under the following conditions: \(u_{0}\in L^{2}(\mathbb{R}^{d}),\ {\omega_{0}\over r^{d-2}}\in L^{{d\over d-2},\infty}(\mathbb{R}^{d})\) and \(\min\{1,r^{3-d}\}{\omega_{0}\over r^{\alpha}}\in L^{\infty}(\mathbb{R}^{d})\) for some α ∈ (0, 1). Moreover, if the domain is a cylinder or if ω0 is single-signed, we prove the same global regularity result for all d ≥ 3. Additionally, for 3 ≤ d ≤ 6, we obtain the same growth bounds as in [Lim and Jeong, Arch. Ration. Mech. Anal., 249, Paper No. 32, 31 pp. (2025)], without assuming compact support on the initial data.
