“A stationary solution for turbulence shell models”
Martedì 18 Febbraio 2020, ore 11:15 - Aula 2BC30 - Alessandro Montagnani
The focus of the talk is to study well-posedness, with respect to generic Gaussian distributed initial data, in turbulence shell models. In the of state-of-the-art results we have existence of solution for any finite energy initial conditions. Here we show the generic existence of solutions with respect to initial data distributed as Gaussian invariant measures, in "mixed" dyadic and tree-like shell models, extending the classical deterministic results. The existence is given thanks to compactness argument and techniques similar to the ones used by Albeverio and Cruzeiro for Euler equation (and more recently with a different approach by F. Flandoli), adapted to our model. Uniqueness is not provided, and the natural oscillating behaviour of the solutions obtained may suggests that it doesn’t hold at all.