Marchioro, Carlo; Maffei, Carlotta A confinement result for axisymmetric fluids. (English) Zbl 1165.76318 Rend. Semin. Mat. Univ. Padova 105, 125-137 (2001). Summary: We consider an incompressible, inviscid, axisymmetric fluid moving in \(\mathbb{R}^3\) without swirl (a vortex ring). We study its time evolution via the Euler equation, assuming that initially the vorticity is concentrated at a finite distance, say \(r_0\), from the symmetry axis. We prove a bound on the growth of the support of the vorticity. Namely we show that the fluid is confined in a cylinder with radius \(r\leq r_0+\text{constant}\,t^{1/4}\log(e+t)\). Cited in 4 Documents MSC: 76B75 Flow control and optimization for incompressible inviscid fluids 76B47 Vortex flows for incompressible inviscid fluids 35Q35 PDEs in connection with fluid mechanics PDFBibTeX XMLCite \textit{C. Marchioro} and \textit{C. Maffei}, Rend. Semin. Mat. Univ. Padova 105, 125--137 (2001; Zbl 1165.76318) Full Text: Numdam EuDML References: [1] J.S. Turner , The flow into an expanding spherical vortex , J. Fluid Mech. , 18 ( 1963 ), pp. 195 - 208 . Zbl 0116.42001 · Zbl 0116.42001 · doi:10.1017/S0022112064000155 [2] G.I. Taylor , Flow induced by jets , J. Aerosp. Sci. , 25 ( 1958 ), pp. 464 - 65 . [3] E.A. Muller - F. Obermeier , Vortex sound , Fluid Dyn. Res. , 3 ( 1988 ), 43 - 65 . [4] T. Minota - T. Kambe - T. Murakami , Acoustic emission from interaction of a vortex ring with a sphere , Fluid Dyn. Res. , 3 ( 1988 ), pp. 357 - 62 . [5] G.W. Rayfield - F. Reif , Evidence for the creation of vortex rings in super-fluid helium , Phys. Rev. Lett. , 11 ( 1963 ), pp. 305 - 8 . [6] K. Shariff - A. LEONARD, Vortex rings , Annu. Rev. Fluid Mech. , 24 ( 1992 ), pp. 235 - 79 . MR 1145011 | Zbl 0743.76024 · Zbl 0743.76024 [7] C. Marchioro , Bounds on the growth of the support of a vortex patch , Comm. Math. Phys. , 164 ( 1994 ), pp. 507 - 24 . Article | MR 1291243 | Zbl 0839.76010 · Zbl 0839.76010 · doi:10.1007/BF02101489 [8] P. Serfati , Borne en temps des carateristiques de l’equation d’Euler 2D a’ tourbillon positif et localisation pour le modele point-vortex , Preprint 1998 . [9] D. Iftimie - T. Sideris - P. Gamblin , On the planar evolution of compactly supported planar vorticity , Comm. in Part. Diff. Eqns. , 24 ( 1999 ), pp. 1709 - 30 . MR 1708106 | Zbl 0937.35137 · Zbl 0937.35137 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.