Uniqueness of Plane Stationary Navier–Stokes Flow Past an Obstacle

Abstract

We study the exterior problem for stationary Navier–Stokes equations in two dimensions describing a viscous incompressible fluid flowing past an obstacle. It is shown that, at small Reynolds numbers, the classical solutions constructed by Finn and Smith are unique in the class of D-solutions (that is, solutions with finite Dirichlet integral). No additional symmetry or decay assumptions are required. This result answers a long-standing open problem. In the proofs, we developed the ideas of the classical Ch. Amick paper (Acta Math. 1988).