On the structure of stationary solutions of the

This paper is a supplementary section to [1]. We show that without any additional hypothesis the main result in [1] (Theorem 1) can be considerably strengthened. Note: This paper can not be read independently of [1]. The numbering of equations, theorems and propositions as well as cross-references used here have to be understood as if this paper were an additional section to [1]. 6 Improved version of Theorem 1 In this supplementary section we show that, without changing the hypotheses, Theorem 1 can be replaced by the following theorem. Theorem 18 (Improved version of Theorem 1) Let and as de ned above. Then, for each u = (u ; v ) in a certain set of vector elds S to be de ned later on, there exist a (locally unique) vector eld u = u1+(u; v) and a function p satisfying the Navier-Stokes equations (1) and (2) in and the boundary conditions (3) and (4). Furthermore, lim x!1 x 1=2 sup y2R j(u u0) (x; y)j = 0 ; (69) lim x!1 x sup y2R j(v v0) (x; y)j = 0 ; (70) where u0(x; y) = c 2 p 1 p x e y 2 4x + d x x2 + y2 ; (71) v0(x; y) = c 4 p y x3=2 e y 2 4x + d y x2 + y2 ; (72) Supported in part by the Fonds National Suisse.