Extension of Hamel paradox for the 2D exterior Navier-Stokes problem

Fuente: arXiv
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Main Authors: Guo, Zhengguang, Hillairet, Matthieu
Format: Preprint
Published: 2024
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author Guo, Zhengguang
Hillairet, Matthieu
author_facet Guo, Zhengguang
Hillairet, Matthieu
contents In this paper, we continue the analysis of the stationary exterior Navier-Stokes problem with interior boundary data and vanishing condition at infinity. We first show an existence result that extends a previous contribution of the second author by considering boundary data prescribing a non-trivial flux on the internal boundary. We obtain in particular that the non-uniqueness result of G. Hamel extends to an open set of internal boundary data. We then show that one way to recover uniqueness of a solution is to complement the perturbation of velocity field with a decay condition at infinity for small circulation through the interior boundary. Our method is based on a fine analysis of the linearized Navier-Stokes system around potential flows in the exterior domain.
format Preprint
id arxiv_https___arxiv_org_abs_2412_17399
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Extension of Hamel paradox for the 2D exterior Navier-Stokes problem
Guo, Zhengguang
Hillairet, Matthieu
Analysis of PDEs
In this paper, we continue the analysis of the stationary exterior Navier-Stokes problem with interior boundary data and vanishing condition at infinity. We first show an existence result that extends a previous contribution of the second author by considering boundary data prescribing a non-trivial flux on the internal boundary. We obtain in particular that the non-uniqueness result of G. Hamel extends to an open set of internal boundary data. We then show that one way to recover uniqueness of a solution is to complement the perturbation of velocity field with a decay condition at infinity for small circulation through the interior boundary. Our method is based on a fine analysis of the linearized Navier-Stokes system around potential flows in the exterior domain.
title Extension of Hamel paradox for the 2D exterior Navier-Stokes problem
topic Analysis of PDEs
url https://arxiv.org/abs/2412.17399