Leray's plane stationary solutions at small Reynolds numbers

Abstract

In the celebrated 1933 paper [22] by J. Leray, 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, as well as the ideas developed in the recent works [19,20].