Uniqueness of Leray solutions of the 3D Navier-Stokes equations is a challenging open problem. In this article we will study this problem for the 3D stationary Navier-Stokes equations in the whole space ${\mathbb{R}}^3$. Under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the trivial solution $\overrightarrow{U}=0$ is the unique solution. This type of results are known as Liouville theorems.

中文翻译：

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Lebesgue和Morrey空间中固定Navier-Stokes方程的一些Liouville定理

3D Navier-Stokes方程的Leray解的唯一性是一个充满挑战的开放问题。在本文中，我们将针对整个空间中的3D平稳Navier-Stokes方程研究此问题${\mathbb{[R}}^3$。在以Lebesgue和Morrey空间表示的其他一些假设下，我们将证明平凡的解$\overrightarrow{ü}=0$是独特的解决方案。这种结果称为Liouville定理。