Unique solvability for the stationary Navier-Stokes equations in exterior domains

In this talk, we present a unique solvability result for the stationary Navier-Stokes equations in an exterior domain Ω in R³, where the external force is given by div F with F = F(x) = (F i j (x)) i,j=1,2,3 . Our main result is the existence and uniqueness of a weak solution for F ∈ L 3/2,∞ (Ω)∩L₂(Ω) provided ∥F∥L 3/2,∞(Ω) is sufficiently small. This weak solution is also unique in the class of weak solutions satisfying the energy inequality, the existence of which was proved by Leray in 1933.