  This short note serves as an introduction to the papers arXiv:1711.01651 and
arXiv:1711.04486 by Maekawa, Miura and Prange. These two works deal with the
existence of mild solutions on the one hand and local energy weak solutions on
the other hand to the Navier-Stokes equations in the half-space $\R^3_+$. We
emphasize a concentration result for (sub)critical norms near a potential
singularity. The contents of these notes were presented during the X-EDP
seminar at IH\'ES in October 2017.
