  We study the survival of charmonium states in a strongly-coupled quark-gluon
plasma in the presence of dissipative forces. We consider first-order
dissipative corrections to the plasma equation of motion in the Bjorken
boost-invariant expansion with a strongly-coupled equation of state for QGP and
study the survival of these states with the dissociation temperatures obtained
by correcting the full Cornell potential not its Coulomb part alone with a
dielectric function encoding the effects of deconfined medium. We further
explore the sensitivity of prompt and sequential suppression of these states to
the shear viscosity-to-entropy density ratio, $\eta/s$ from perturbative QCD
and AdS/CFT predictions. Our results show excellent agreement with the recent
experimental results at RHIC.
