  Cooperativity effects have been proposed to explain the non-local rheology in
the dynamics of soft jammed systems. Based on the analysis of the free-energy
model proposed by L. Bocquet, A. Colin \& A. Ajdari ({\em Phys. Rev. Lett.}
{\bf 103}, 036001 (2009)), we show that cooperativity effects resulting from
the non-local nature of the fluidity (inverse viscosity), are intimately
related to the emergence of shear-banding configurations. This connection
materializes through the onset of inhomogeneous compact solutions (compactons),
wherein the fluidity is confined to finite-support subregions of the flow and
strictly zero elsewhere. Compactons coexistence with regions of zero fluidity
("non-flowing vacuum") is shown to be stabilized by the presence of mechanical
noise, which ultimately shapes up the equilibrium distribution of the fluidity
field, the latter acting as an order parameter for the flow-noflow transitions
occurring in the material.
