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In this paper we prove Liouville type theorem for the stationary Navier–Stokes equations in $$\mathbb {R}^3$$ 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 $$u(x) \rightarrow 0$$ u ( x ) → 0 as $$|x|\rightarrow +\infty $$ | x | → + ∞ and the condition of finite Dirichlet integral $$\int _{\mathbb {R}^3} | \nabla u|^2 dx <+\infty $$ ∫ R 3 | ∇ u | 2 d x < + ∞ is trivial, if either $$|u(x)|/|Q(x)|=O(1)$$ | u ( x ) | / | Q ( x ) | = O ( 1 ) or $$|p(x)|/|Q(x)| =O(1) $$ | p ( x ) | / | Q ( x ) | = O ( 1 ) as $$|x|\rightarrow \infty $$ | x | → ∞ , where $$|Q|=\frac{1}{2} |u|^2 +p$$ | Q | = 1 2 | u | 2 + p is the head pressure.

Relative Decay Conditions on Liouville Type Theorem for the Steady Navier–Stokes System