  In the celebrated paper by Jean Leray, published in JMPA journal in 1933, the
invading domains method was proposed to construct D-solutions for the
stationary Navier-Stokes flow around obstacle problem. In two dimensions,
whether Leray's D-solution achieves the prescribed limiting velocity at spatial
infinity became a major open problem since then. In this paper, we solve this
problem at small Reynolds numbers. The proof builds on a novel blow-down
argument which rescales the invading domains to the unit disc, and the ideas
developed in a recent paper [Korobkov-Pileckas-Russo2020], where the
nontriviality of Leray solutions in the general case was proved, and
[Korobkov-Ren-2021], where the uniqueness result for small Reynolds number was
established.
