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arXiv: 0905.1854

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Electronic Journal of Probability 14, 89 (2009) 2551-2579

Available versions:

v1 (2009-05-12)

v2 (2009-11-29)

Large deviation principle and inviscid shell models

Hakima Bessaih 1, Annie Millet 2, 3, 4

(2009-11-26)

A LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient converges to 0 and the noise intensity is multiplied by the square root of the viscosity, we prove that some shell models of turbulence with a multiplicative stochastic perturbation driven by a H-valued Brownian motion satisfy a LDP in C([0,T],V) for the topology of uniform convergence on [0,T], but where V is endowed with a topology weaker than the natural one. The initial condition has to belong to V and the proof is based on the weak convergence of a family of stochastic control equations. The rate function is described in terms of the solution to the inviscid equation.

1:	Department of Mathematics, University of Wyoming
	University
2:	Centre d'économie de la Sorbonne (CES)
	CNRS : UMR8174 – Université Paris I - Panthéon-Sorbonne
3:	Statistique Appliquée et MOdélisation Stochastique (SAMOS)
	Université Paris I - Panthéon-Sorbonne
4:	Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
	CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot

Subject

:

Mathematics/Probability

Keyword(s): Shell models of turbulence – viscosity coefficient and inviscid models – stochastic PDEs – large deviations

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From: Annie Millet <>

Submitted on: Sunday, 29 November 2009 00:21:55

Updated on: Monday, 30 November 2009 10:49:33