On Liouville type theorem for the stationary Navier–Stokes equations.

In this paper we prove a Liouville type theorem for the stationary Navier–Stokes equations in R 3 . Let V = (V ij) be a potential function of a smooth solution u, which means u = ∇ · V . We show that if there exists 3 < s < + ∞ such that the L s mean oscillation of the potential function has certain growth condition near infinity, namely 1 | B (r) | ∫ B (r) | V - V B (r) | s d x ≤ C r min { s - 3 3 , s 6 } ∀ 1 < r < + ∞ , then u ≡ 0 . [ABSTRACT FROM AUTHOR]