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arXiv · 2412.17399

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

Zhengguang Guo·Matthieu Hillairet
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Abstract

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.

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Zhengguang Guo, Matthieu Hillairet. 2024-12-23. Extension of Hamel paradox for the 2D exterior Navier-Stokes problem. https://arxiv.org/abs/2412.17399

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