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arXiv · 2105.08898

Leray's plane stationary solutions at small Reynolds numbers

Mikhail V. Korobkov·Xiao Ren
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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.

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Mikhail V. Korobkov, Xiao Ren. 2021-05-19. Leray's plane stationary solutions at small Reynolds numbers. https://arxiv.org/abs/2105.08898

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