  We consider an incompressible kinetic Fokker Planck equation in the flat
torus, which is a simplified version of the Lagrangian stochastic models for
turbulent flows introduced by S.B. Pope in the context of computational fluid
dynamics. The main difficulties in its treatment arise from a pressure type
force that couples the Fokker Planck equation with a Poisson equation which
strongly depends on the second order moments of the fluid velocity. In this
paper we prove short time existence of analytic solutions in the
one-dimensional case, for which we are able to use techniques and functional
norms that have been recently introduced in the study of a related singular
model.
