Stationary Stokes and Navier-Stokes systems in an infinite open channel. II
[For Part I, see Lith. Math. J. 29, No. 1, 34--47 (1989); translation from Litov. Mat. Sb. 29, No. 1, 90--108 (1989; Zbl 0703.35149).] In part I the main problems were formulated. Existence and uniqueness theorems are proved for solutions of certain boundary problems related with the stationary Stokes equations, giving a priori estimates in appropriate weighted Sobolev norms, and weighted Hölder norms also. Existence theorems are obtained for generalized solutions of boundary problems related with the stationary Navier-Stokes equations. An adequate representation (according the asymptotics as \(| x| \to \infty)\) of the solution, its uniqueness and a priori estimates in different functional spaces, are given under certain conditions.
scientific article; zbMATH DE number 4175583