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

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

2011-03-10

arxiv.org/abs/1103.2151v1

Physics

Mathematical Physics

Scientific paper

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.

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