In this paper we prove Liouville type theorem for the stationary Navier–Stokes equations in \(\mathbb {R}^3\) under the assumptions on the relative decays of velocity, pressure and the head pressure. More precisely, we show that any smooth solution (u, p) of the stationary Navier–Stokes equations satisfying \(u(x) \rightarrow 0\) as \(|x|\rightarrow +\infty \) and the condition of finite Dirichlet integral \(\int _{\mathbb {R}^3} | \nabla u|^2 dx <+\infty \) is trivial, if either \(|u(x)|/|Q(x)|=O(1)\) or \(|p(x)|/|Q(x)| =O(1) \) as \(|x|\rightarrow \infty \), where \(|Q|=\frac{1}{2} |u|^2 +p\) is the head pressure.

在本文中，我们在速度，压力和头部压力相对衰减的假设下，证明了\（\ mathbb {R} ^ 3 \）中的平稳Navier–Stokes方程的Liouville型定理。更确切地说，我们表明，任何光滑溶液（ü，  p）的Navier-Stokes方程的满足\（U（X）\ RIGHTARROW 0 \）作为\（| \ RIGHTARROW + \ infty \ | X）的条件和有限Dirichlet积分\（\ int _ {\ mathbb {R} ^ 3} | \ nabla u | ^ 2 dx <+ \ infty \）如果是\（| u（x）| / | Q（x） | = O（1）\）或\（| p（x）| / | Q（x）| = O（1）\）为\（| x | \ rightarrow \ infty \），其中\（| Q | = \ frac {1} {2} | u | ^ 2 + p \）是头部压力。