Invariant Measures of Gaussian Type for 2D Turbulence

Invariant Measures of Gaussian Type for 2D Turbulence Article

Bessaih, H, Ferrario, B. (2012). Invariant Measures of Gaussian Type for 2D Turbulence . 149(2), 259-283. 10.1007/s10955-012-0601-z

Gaussian measures μβ, ν are associated to some stochastic 2D models of turbulence. They are Gibbs measures constructed by means of an invariant quantity of the system depending on some parameter β (related to the 2D nature of the fluid) and the viscosity ν. We prove the existence and the uniqueness of the global flow for the stochastic viscous system; moreover the measure μβ, ν is invariant for this flow and is the unique invariant measure. Finally, we prove that the deterministic inviscid equation has a μβ, ν-stationary solution (for any ν > 0). © 2012 Springer Science+Business Media New York.