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- W4367000301 abstract "We consider incompressible Euler equations in any dimension $ dgeq3 $ 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 $ dgeq4 $ remains unsolved. Very 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 $ dgeq4 $. 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." @default.
- W4367000301 created "2023-04-27" @default.
- W4367000301 creator A5034793259 @default.
- W4367000301 date "2023-04-24" @default.
- W4367000301 modified "2023-10-01" @default.
- W4367000301 title "Global regularity of some axisymmetric, single-signed vorticity in any dimension" @default.
- W4367000301 doi "https://doi.org/10.48550/arxiv.2304.12089" @default.
- W4367000301 hasPublicationYear "2023" @default.
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