In this paper we study a stochastic version of an inviscid shell model of turbulence with multiplicative noise. The deterministic counterpart of this model is quite general and includes inviscid GOY and Sabra shell models of turbulence. We prove glob
al weak existence and uniqueness of solutions for any finite energy initial condition. Moreover energy dissipation of the system is proved in spite of its formal energy conservation.
A shell-type model of an inviscid fluid, previously considered in the literature, is investigated in absence of external force. Energy dissipation of positive solutions is proved and decay of energy like $t^{-2}$ is established. Self-similar decaying
positive solutions are introduced and proved to exist and classified. Coalescence and blow-up are obtained as a consequence, in the class of arbitrary sign solutions.
