  The ellipsoidal BGK model was introduced in \cite{Ho} to fit the correct
Prandtl number in the Navier-Stokes approximation of the classical BGK model.
In the paper we establish the global existence of mild solutions to the Cauchy
problem on the model for a class of initial data allowed to have large
oscillations. The proof is motivated by a recent study of the same topic on the
Boltzmann equation in \cite{DHWY}.
