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

Abstract

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,∞ with ∇u∈L3/2,∞, where L3,∞ and L3/2,∞ are the Lorentz spaces. Our criterion asserts that if u and v are the solutions, u is small in L3,∞ and u,v∈Lp for some p>3, then u=v. The proof is based on analysis of the dual equation with the aid of the bootstrap argument.