  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.
