Leray's plane stationary solutions at small Reynolds numbers
Abstract
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.
Keywords
Cite
@article{arxiv.2105.08898,
title = {Leray's plane stationary solutions at small Reynolds numbers},
author = {Mikhail V. Korobkov and Xiao Ren},
journal= {arXiv preprint arXiv:2105.08898},
year = {2021}
}