Invariant Gibbs measures for some 3D and 2D turbulence models

Tuesday, November 27, 2012 - 10:30am - 12:00pm
Lind 305
Hakima Bessaih (University of Wyoming)
Inside the analysis of equations of hydrodynamic, statistical solutions have been investigated. In fact, the individual solutions may give a detailed and too complicated picture of the fluid, while one could be interested in the behavior of some global quantity related to the fluid, where the microscopic picture is replaced by the macroscopic one. This is the statistical approach to turbulence. From the mathematical point of view, we are interested in distributions invariant for these flows. Gaussian measures of Gibbsian type are associated with some shell models of 3D turbulence and 2D turbulence (GOY and SABRA models). 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 these flows.