Large deviation principle and inviscid shell models Article

Bessaih, H, Millet, A. (2009). Large deviation principle and inviscid shell models . 14 2551-2579. 10.1214/EJP.v14-719

cited authors

  • Bessaih, H; Millet, A

authors

abstract

  • 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 √ 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. © 2009 Applied Probability Trust.

publication date

  • January 1, 2009

Digital Object Identifier (DOI)

start page

  • 2551

end page

  • 2579

volume

  • 14