Solenoidal extensions of vector fields in two-dimensional unbounded domains

The goal of this note is to construct solenoidal extensions of vector fields defined on the boundary of simply connected domains having outlets to infinity and which satisfy the Leray-Hopf condition. The case of non-simply connected domains is also mentioned, in particular in the case when the domain admits a symmetry axis. This kind of extensions allows us to solve the stationary Navier-Stokes problem with nonhomogeneous boundary conditions in such domains. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.