We study the three‐dimensional stationary exterior Stokes problem with non standard boundary conditions corresponding to a slip‐without‐friction boundary conditions. Because the flow domain is unbounded, we set the problem in weighted spaces in order to control the behavior at infinity of solutions. This functional framework allows to prescribe various behaviors at infinity of the solutions. The established results are related to the existence and the uniqueness of strong and very weak solutions. Our strategy relies on the fact that due to the boundary conditions, the pressure and the velocity can be decoupled and, as a result, we solve two separate systems to find these quantities.

中文翻译：

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非标准边界条件下的三维静态外部斯托克斯问题

我们研究了与非滑动边界条件相对应的具有非标准边界条件的三维静态外部斯托克斯问题。因为流域是无界的，所以我们在加权空间中设置问题，以便控制无穷大的行为。该功能框架允许规定解决方案无穷大的各种行为。确定的结果与强和非常弱的解决方案的存在和唯一性有关。我们的策略基于以下事实：由于边界条件，压力和速度可以解耦，因此，我们解决了两个单独的系统以找到这些量。