Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces

Abstract

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.