  We explicitly take into account the effect of hydrodynamic expansion profile
on the gluonic breakup of $J/\psi$'s produced in an equilibrating parton
plasma. Attention is paid to the space-time inhomogeneities as well as Lorentz
frames while deriving new expressions for the gluon number density $n_g$,
average dissociation rate $<\tilde{\Gamma}>$, and $\psi$ survival probability
$S$. A novel type of partial wave {\em interference} mechanism is found to
operate in the formula of $<\tilde{\Gamma}>$. Nonrelativistic longitudinal
expansion fro small length of the initial cylinder is found to push the
$S(p_T)$ graph above the no flow case considered by us earlier \cite{rev1}.
However, relativistic flow corresponding to large length of the initial
cylinder pushes the curve of $S(p_T)$ downwards at LHC but upwards at RHIC.
This mutually different effect on $S(p_T)$ may be attributed to the different
initial temperatures generated at LHC and RHIC.
