Fraenkel, L. E.; Preston, M. D. On a singular initial-value problem for the Navier-Stokes equations. (English) Zbl 1320.35256 Mathematika 61, No. 2, 277-294 (2015). Summary: This paper presents a recent result for the problem introduced eleven years ago by L. E. Fraenkel and J. B. McLeod [“A diffusing vortex circle in a viscous fluid”, in: IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, 489–500 (2003; Zbl 1131.74003)], but described only briefly there. We shall prove the following, as far as space allows. The vorticity \(\omega\) of a diffusing vortex circle in a viscous fluid has, for small values of a non-dimensional time, a second approximation \(\omega_{A}+\omega_{1}\) that, although formulated for a fixed, finite Reynolds number \(\lambda\) and exact for \(\lambda = 0\) (then \(\omega = \omega_{A}\)), tends to a smooth limiting function as \(\lambda \uparrow \infty\). In \({\S}{\S}1\) and 2 the necessary background and apparatus are described; \({\S}3\) outlines the new result and its proof. MSC: 35Q30 Navier-Stokes equations 35B25 Singular perturbations in context of PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids 76D17 Viscous vortex flows Citations:Zbl 1131.74003 PDFBibTeX XMLCite \textit{L. E. Fraenkel} and \textit{M. D. Preston}, Mathematika 61, No. 2, 277--294 (2015; Zbl 1320.35256) Full Text: DOI References: [1] Watson, Theory of Bessel Functions (1952) [2] Fraenkel, IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics pp 489– (2003) [3] Saffman, Stud. Appl. Math. 49 pp 371– (1970) · Zbl 0224.76032 · doi:10.1002/sapm1970494371 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.