## Electronic Journal of Probability

### Large Deviation Principle and Inviscid Shell Models

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 89, 2551-2579.

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

https://projecteuclid.org/euclid.ejp/1464819550

Digital Object Identifier
doi:10.1214/EJP.v14-719

Mathematical Reviews number (MathSciNet)
MR2570011

Zentralblatt MATH identifier
1191.60074

Rights

#### Citation

Bessaih, Hakima; Millet, Annie. Large Deviation Principle and Inviscid Shell Models. Electron. J. Probab. 14 (2009), paper no. 89, 2551--2579. doi:10.1214/EJP.v14-719. https://projecteuclid.org/euclid.ejp/1464819550

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