Open Access
2009 Large Deviation Principle and Inviscid Shell Models
Hakima Bessaih, Annie Millet
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Electron. J. Probab. 14: 2551-2579 (2009). DOI: 10.1214/EJP.v14-719


LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient converges to 0 and the noise intensity is multiplied by its square root, we prove that some shell models of turbulence with a multiplicative stochastic perturbation driven by a $H$-valued Brownian motion satisfy a LDP in $\mathcal{C}([0,T],V)$ 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.


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Hakima Bessaih. Annie Millet. "Large Deviation Principle and Inviscid Shell Models." Electron. J. Probab. 14 2551 - 2579, 2009.


Accepted: 26 November 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1191.60074
MathSciNet: MR2570011
Digital Object Identifier: 10.1214/EJP.v14-719

Primary: 60H15
Secondary: 60F10 , 76D06 , 76M35

Keywords: large deviations , Shell models of turbulence , stochastic PDEs , viscosity coefficient and inviscid models

Vol.14 • 2009
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