  This paper deals with the study of some particular kinetic models, where the
randomness acts only on the velocity variable level. Usually, the Markovian
generator cannot satisfy any Poincar\'e's inequality. Hence, no Gronwall's
lemma can easily lead to the exponential decay of Ft (the L2 norm of a test
function along the semi-group). Nevertheless for the kinetic Fokker-Planck
dynamics and for a piecewise deterministic evolution we show that Ft satisfies
a third order differential inequality which gives an explicit rate of
convergence to equilibrium.
