标题： Hamel悖论在二维外部Navier-Stokes问题中的扩展 显示英文标题

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

摘要： 在本文中，我们继续分析具有内部边界数据和无穷远处消失条件的定常外部纳维-斯托克斯问题。我们首先展示了一个存在性结果，该结果扩展了第二作者之前的贡献，考虑了在内部边界上规定非零通量的边界数据。我们特别得到，G. Hamel的非唯一性结果可以扩展到内部边界数据的一个开集。然后我们表明，恢复解的唯一性的一种方法是通过在内部边界上的小环量补充速度场的扰动和无穷远处的衰减条件。我们的方法基于对外部区域中势流周围线性化纳维-斯托克斯系统的精细分析。 显示英文摘要

摘要： 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.