  We consider incompressible Euler equations in any dimension $ d\geq3 $
imposing axisymmetric symmetry without swirl. While the global regularity of
smooth flows in this setting has been well-known in $ d=3 $, the same question
in higher dimensions $ d\geq4 $ remains unsolved. Recently, global regularity
for the case $ d=4 $ with some extra decay assumption on vorticity is obtained
by proving global estimate of the radial velocity. Now we prove that the
vorticity with single-sign and a similar decay assumption is globally regular
for any $ d\geq4 $. This is due to pointwise decay estimate of radial velocity
in sufficiently large radial distance, which depends on time. The result is of
confinement type for support growth, which is going back to Marchioro [Comm.
Math. Phys., 164 (1994) 507-524] and Iftimie--Sideris--Gamblin [Comm. Partial
Differential Equations, 24 (1999) 1709-1730] for $ \mathbb{R}^{2} $. In
particular, we follow the approach of Maffei--Marchioro [Rend. Sem. Mat. Univ.
Padova, 105 (2001) 125-137] for $ d=3 $ so that we generalize the confinement
into any dimension.
