Some Liouville-type theorems for the stationary density-dependent Navier–Stokes equations

This paper is devoted to the Liouville-type theorems for the 3D stationary density-dependent Navier–Stokes equations, without any integrability assumption on ∇u. More precisely, we prove that the velocity field u, being in some Lorentz spaces, must be zero, provided the density ρ is essentially bounded.