An inviscid dyadic model of turbulence: the fixed point and Onsager's conjecture

Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the 3-dimensional scaling of the quadratic nonlinearity. It is proved that the system with forcing has a unique equilibrium and that every solution blows up in finite time in $H^{5/6}$-norm. Onsager's conjecture is confirmed for the model system.