The inviscid limit of 2D Navier-Stokes near a self-similar vortex collapse

We study the inviscid limit of the two-dimensional Navier–Stokes equations with initial vorticity given by three point vortices whose inviscid trajectories collapse self-similarly at $t=1$. For every fixed $0<\gamma <1$, we prove that the solution is approximated by a superposition of Lamb–Oseen vortices centered at the point-vortex positions, with an $L^1$ error of order $O({\nu }^{1-\gamma })$, uniformly for $0<t\le T_{\nu }=1-{\nu }^{\gamma }$. We use coordinates adapted to the self-similar collapse and study a long-time inviscid limit problem on the interval $0<s\le \gamma \log (1\mathrm{/}\nu )$, with a time-dependent rescaled diffusion coefficient $\eta (s)$ that tends to zero as $s\to \mathrm{\infty }$.