  We study a new flocking model which has the versatility to capture the
physically realistic qualitative behavior of the Motsch-Tadmor model, while
also retaining the entropy law, which lends to a similar 1D global
well-posedness analysis to the Cucker-Smale model. This is an improvement to
the situation in the Cucker-Smale case, which may display the physically
unrealistic behavior that large flocks overpower the dynamics of small, far
away flocks; and it is an improvement in the situation in the Motsch-Tadmor
case, where 1D global well-posedness is not known. The new model was proposed
in arXiv:2211.00117v3 and has a similar structure to the Cucker-Smale and
Motsch-Tadmor hydrodynamic systems, but with a new feature: the communication
strength is not fixed, but evolves in time according to its own transport
equation along the Favre-filtered velocity field. This transport of the
communication strength is precisely what preserves the entropy law. A variety
of phenomenological behavior can be obtained from various choices of the
initial communication strength, including the aforementioned Motsch-Tadmor-like
behavior. We develop the general well-posedness theory for the new model and
study the long time behavior -- including alignment, strong flocking in 1D, and
entropy estimates to estimate the distribution of the limiting flock, all of
which extend the classical results of the Cucker-Smale case. In addition, we
provide numerical evidence to show the similar qualitative behavior
