  The aim of this paper is to give a detailed presentation of long wave
instabilities of shear layers for Navier Stokes equations, and in particular to
give a simple and easy to read presentation of the study of Orr Sommerfeld
equation and to detail the analysis of its adjoint. Using these analyses we
prove the existence of long wave instabilities in the case of slowly rotating
fluids, slightly compressible fluids and for Navier boundary conditions, under
smallness conditions.
