Invariant Gibbs measures of the energy for shell models of turbulence: The inviscid and viscous cases Article

Bessaih, H, Ferrario, B. (2012). Invariant Gibbs measures of the energy for shell models of turbulence: The inviscid and viscous cases . NONLINEARITY, 25(4), 1075-1097. 10.1088/0951-7715/25/4/1075

cited authors

  • Bessaih, H; Ferrario, B

authors

abstract

  • Gaussian measures of Gibbsian type are associated with some shell model of 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 with the property that these Gibbs measures are invariant for this flow. Moreover, we prove that the deterministic inviscid shell model has a stationary solution with respect to these measures. © 2012 IOP Publishing Ltd & London Mathematical Society.

publication date

  • April 1, 2012

published in

Digital Object Identifier (DOI)

start page

  • 1075

end page

  • 1097

volume

  • 25

issue

  • 4