Local existence of analytical solutions to an incompressible Lagrangian   stochastic model in a periodic domain
  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. 
Mireille Bossy, Joaquin Fontbona, Pierre-Emmanuel Jabin and   Jean-Fran\c{c}ois Jabir
math-ph math.MP