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

Abstract : We consider an incompressible kinetic Fokker Planck equation in the flat torus. This equation is a simplified version of the Lagrangian stochastic models for turbulent flows introduced by S.B. Pope in the context of computational fluid mechanics. The main difficulties in its treatment arise from the pressure type force in the equation that couples the Fokker Planck equation with a Poisson equation. We prove short time existence of analytic solutions in the one-dimensional case, where we are able to explicit the pressure force and use techniques and functional norms recently introduced in the study of a related singular model.
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Mireille Bossy, Joaquin Fontbona, Pierre-Emmanuel Jabin, Jean Francois Jabir. Local existence of analytical solutions to an incompressible Lagrangian stochastic model in a periodic domain. Communications in Partial Differential Equations, Taylor & Francis, 2013, 38 (7), pp.1141-1182. ⟨10.1080/03605302.2013.786727⟩. ⟨hal-00691712v2⟩

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