2013 年 56 巻 2 号 p. 323-337
We consider the uniqueness of stationary solutions to the 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. It is shown that if solutions u and v satisfy the conditions that u is small in L3, ∞ and v ∈ L3 + L∞, then u = v. The proof relies upon the regularity theory for the perturbed Stokes equation.