A remark on the existence of 2-D steady Navier-Stokes flow in bounded symmetric domain under general outflow condition (Q2460213)

Consider the stationary two-dimensional Navier-Stokes equations on a bounded domain, symmetric with respect to the \(x_2\)-axis, such that each connected component of the boundary intersects the \(x_2\)-axis and such that the boundary data are also symmetric with respect to the \(x_2\)-axis. \textit{C. J. Amick} [Indiana Univ. Math. J. 33, 817--830 (1984; Zbl 0563.35059)] and \textit{H. Fujita} [Navier-Stokes equations. Theory and numerical methods. Proceedings of the international conference, Varenna, Lecco, Italy, June 2-6, 1997. Harlow: Longman. Pitman Res. Notes Math. Ser. 388, 16--30 (1998; Zbl 0946.35063)] proved the existence of symmetric solutions when the boundary value satisfies a general outflow condition. Fujita's work was based on a theorem about the solenoidal extension of the boundary data. The publication under review gives an alternative, possibly more elementary proof of this result.