“…The study is partly motivated by the related Liouville problem of the stationary Navier-Stokes equations, which has attracted much attention in recent years and is still far from being fully understood. See for example [1,2,3,4,5,7,8,9,12,13] and the reference therein. First, in full 3D case, the Liouville-type theorem holds provided the vanishing of u θ and h θ .…”