Title: The Faber-Krahn inequality for the Stokes operator

Abstract: In this work in collaboration with A. Henrot and Y. Privat, we investigate the minimisation of the first eigenvalue of the Dirichlet-Stokes operator in $mathbb R^d$. To be more specific, we consider the question of existence of optimal shapes, a query made more difficult by the incompressibility constraint, as well as the minimality of the ball. This latter point turns out to be dependent on the dimension, and starkly different from the case of the (scalar) Dirichlet-Laplacian.