caa a22 4500 605515204 CHVBK 20210128100708.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s00205-014-0775-4 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0775-4 On the Cauchy Problem for Axi-Symmetric Vortex Rings [Elektronische Daten] [Hao Feng, Vladimír Šverák] We consider the classical Cauchy problem for the three dimensional Navier-Stokes equation with the initial vorticity ω 0 concentrated on a circle, or more generally, a linear combination of such data for circles with common axis of symmetry. We show that natural approximations of the problem obtained by smoothing the initial data satisfy good uniform estimates which enable us to conclude that the original problem with the singular initial distribution of vorticity has a solution. We impose no restriction on the size of the initial data. Springer-Verlag Berlin Heidelberg, 2014 Feng Hao University of Minnesota, Minneapolis, USA aut Šverák Vladimír University of Minnesota, Minneapolis, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/1(2015-01-01), 89-123 0003-9527 215:1<89 2015 215 205 https://doi.org/10.1007/s00205-014-0775-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0775-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Feng Hao University of Minnesota, Minneapolis, USA aut NATIONALLICENCE 700 1- Šverák Vladimír University of Minnesota, Minneapolis, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/1(2015-01-01), 89-123 0003-9527 215:1<89 2015 215 205