On uniqueness of stationary solutions to the Navier–Stokes equations in exterior domains

The aim of this paper is to prove a uniqueness criterion for solutions to the stationary Navier–Stokes equation in 3-dimensional exterior domains within the class u∈L3,∞u∈L3,∞ with ∇u∈L3/2,∞∇u∈L3/2,∞, where L3,∞L3,∞ and L3/2,∞L3/2,∞ are the Lorentz spaces. Our criterion asserts that if uu and vv are the solutions, uu is small in L3,∞L3,∞ and u,v∈Lpu,v∈Lp for some p>3p>3, then u=vu=v. The proof is based on analysis of the dual equation with the aid of the bootstrap argument.