  A model for the slow dynamics of the supercooled liquid is formulated in
terms of the standard equations of fluctuating nonlinear hydrodynamics (FNH)
with the inclusion of an extra diffusive mode for the collective density
fluctuations. If the compressible nature of the liquid is completely ignored,
this diffusive mode sets the longest relaxation times in the supercooled state
and smooths off a possible sharp ergodicity-nonergodicity (ENE) transition
predicted in a mode coupling theory. The scenario changes when the complete
dynamics is considered with the inclusion of $1/\rho$ nonlinearities in the FNH
equations, reflecting the compressible nature of the liquid. The latter
primarily determines the extent of slowing down in the supercooled liquid. The
presence of slow diffusive modes in the supercooled liquid do not give rise to
very long relaxation times unless the role of couplings between density and
currents in the compressible liquid is negligible.
