  In this note we show a Kawamata-Viehweg vanishing theorem for pl-contractions
on threefolds in characteristic $p>5$. We deduce several applications for klt
threefolds: the vanishing of higher direct images of structure sheaves of Mori
fibre spaces, Koll\'ar's result on local vanishing and the rationality of the
singularities of the base of a conic bundle.
