Invariant Gibbs measures of the energy for shell models of turbulence; the inviscid and viscous cases

Abstract

Gaussian measures of Gibbsian type are associated with some shell models of 3D turbulence; they are constructed by means of the energy, a conserved quantity for the 3D inviscid and unforced shell model. We prove the existence of a unique global flow for a stochastic viscous shell model and a global flow for the deterministic inviscid shell model, with the property that these Gibbs measures are invariant for these flows.

References in corpus (2)

• Stochastic 2D hydrodynamical type systems: Well posedness and large deviations
• A Note on the Regularity of Inviscid Shell Model of Turbulence

Cited by in corpus (4)

• Numerical approximation of stochastic evolution equations: Convergence in scale of Hilbert spaces
• Dyadic models for fluid equations: a survey
• Stochastic inviscid shell models: well-posedness and anomalous dissipation
• Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with Lévy noise