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Large Deviation Principle and Inviscid Shell Models

Bessaih, Hakima
Millet, A.
Abstract
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A LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient v converges to 0 and the noise intensity is multiplied by root v, 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.
Date
2009-11-26
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University of Wyoming. Libraries
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Keywords
Shell models of turbulence , viscosity coefficient and inviscid models , stochastic PDEs , large deviations , Mathematics
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