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

2012/04/26 by Mireille Bossy, Joaquin Fontbona, Bossy, Mireille +5
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1204.6056

32 pages

arxiv created 2013/03/16 · arxiv updated 2013/03/19

Abstract

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.

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