@article{EJP719,
author = {Hakima Bessaih and Annie Millet},
title = {Large Deviation Principle and Inviscid Shell Models},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {14},
year = {2009},
keywords = {Shell models of turbulence; viscosity coefficient and inviscid models; stochastic PDEs; large deviations},
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.},
pages = {no. 89, 2551-2579},
issn = {1083-6489},
doi = {10.1214/EJP.v14-719},
url = {http://ejp.ejpecp.org/article/view/719}}