On the Liouville theorem for the stationary Navier–Stokes equations in a critical space

In this paper we prove the Liouville type theorem for the stationary Navier–Stokes equations on R 3 . More specifically, if a solution u ∈ H ̇ 1 ( R 3 ) to the stationary Navier–Stokes system satisfies additional conditions characterized by the decays near infinity and by the oscillation, then we show that u = 0 .