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We consider an incompressible kinetic Fokker Planck equation in the flattorus, which is a simplified version of the Lagrangian stochastic models forturbulent flows introduced by S.B. Pope in the context of computational fluiddynamics. The main difficulties in its treatment arise from a pressure typeforce that couples the Fokker Planck equation with a Poisson equation whichstrongly depends on the second order moments of the fluid velocity. In thispaper we prove short time existence of analytic solutions in theone-dimensional case, for which we are able to use techniques and functionalnorms that have been recently introduced in the study of a related singularmodel.

Local existence of analytical solutions to an incompressible Lagrangian stochastic model in a periodic domain