  We consider the global evolution problem for a model which couples together a
nonlinear wave equation and a nonlinear Klein-Gordon equation, and was
independently introduced by LeFloch and Y. Ma and by Q. Wang. By revisiting the
Hyperboloidal Foliation Method, we establish that a weighted energy of the
solutions remains (almost) bounded for all times. The new ingredient in the
proof is a hierarchy of fractional Morawetz energy estimates (for the wave
component of the system) which is defined from two conformal transformations.
The optimal case for these energy estimates corresponds to using the scaling
vector field as a multiplier for the wave component.
