TY - JOUR
T1 - Local Existence of Analytical Solutions to an Incompressible Lagrangian Stochastic Model in a Periodic Domain
AU - Bossy, Mireille
AU - Fontbona, Joaquin
AU - Jabin, Pierre Emmanuel
AU - Jabir, Jean François
N1 - Funding Information:
We would like to thank the anonymous referees for carefully reading a previous version of this work, for helpful suggestions in order to improve its presentation and for pointing out a gap in one of the proofs. J. Fontbona was partially supported by Fondecyt Grant 1110923 and Basal-Conicyt-Chile; J.-F. Jabir was partially supported by Fondecyt Grant 3100132 and Conicyt PAI/ACADEMIA 79090016.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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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U2 - 10.1080/03605302.2013.786727
DO - 10.1080/03605302.2013.786727
M3 - Article
AN - SCOPUS:84879624198
SN - 0360-5302
VL - 38
SP - 1141
EP - 1182
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 7
ER -