ON A SINGULAR INITIAL‐VALUE PROBLEM FOR THE NAVIER–STOKES EQUATIONS

This paper presents a recent result for the problem introduced eleven years ago by Fraenkel and McLeod [A diffusing vortex circle in a viscous fluid. In IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics , Kluwer (2003), 489–500], but described only briefly there. We shall prove the following, as far as space allows. The vorticity ω of a diffusing vortex circle in a viscous fluid has, for small values of a non‐dimensional time, a second approximationω A + ω 1that, although formulated for a fixed, finite Reynolds number λ and exact for λ = 0 (then ω = ω A ), tends to a smooth limiting function as λ ↑ ∞ . In §§1 and 2 the necessary background and apparatus are described; §3 outlines the new result and its proof.