Local Existence of Analytical Solutions to an Incompressible Lagrangian Stochastic Model in a Periodic Domain

Mireille Bossy, Joaquin Fontbona, Pierre Emmanuel Jabin, Jean François Jabir

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1141-1182
Number of pages42
JournalCommunications in Partial Differential Equations
Volume38
Issue number7
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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