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Leray's plane stationary solutions at small Reynolds numbers
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
-
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.
- Subjects :
- Applied Mathematics
General Mathematics
Open problem
media_common.quotation_subject
Mathematical analysis
Mathematics::Analysis of PDEs
Reynolds number
Limiting
Infinity
76D05
Physics::Fluid Dynamics
symbols.namesake
Mathematics - Analysis of PDEs
Flow (mathematics)
Obstacle problem
symbols
FOS: Mathematics
Unit (ring theory)
Mathematics
media_common
Analysis of PDEs (math.AP)
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....919f49d2812eb93fbdcd8b5c177b5608
- Full Text :
- https://doi.org/10.48550/arxiv.2105.08898