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

Mireille Bossy (  Author to contact preferably ) 1, Joaquin Fontbona 2, Pierre-Emmanuel Jabin 3, Jean Francois Jabir 4

(2012-04-26)

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.

1:	TOSCA (INRIA Sophia Antipolis / INRIA Nancy - Grand Est/ IECN)
	INRIA – CNRS : UMR7502 – Université de Lorraine
2:	Departamento de Ingeniería Matemática [Santiago] (DIM)
	Departamento de Ingeniería Matemática – Universidad de Chile
3:	Center for Scientific Computation and Mathematical Modeling (CSCAMM)
	University of Maryland
4:	Institut de Mathématiques de Toulouse (IMT)
	Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219

Domain

:

Mathematics/Numerical Analysis

Keywords: Fluid particle model – Incompressibility – Analytic solution – Singular kinetic equation.

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From: Mireille Bossy <>

Submitted on: Thursday, 26 April 2012 20:11:22

Updated on: Tuesday, 13 November 2012 15:15:05