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 R3R3. More specifically, if a solution u∈Ḣ1(R3) to the stationary Navier–Stokes system satisfies additional conditions characterized by the decays near infinity and by the oscillation, then we show that u=0u=0.