We find a strong evidence for the survival of $J/Psi$ and $eta_c$ as spatially-localized $cbar c$ (quasi-)bound states above the QCD critical temperature $T_c$, by investigating the boundary-condition dependence of their energies and spectral functio
ns. In a finite-volume box, there arises a boundary-condition dependence for spatially spread states, while no such dependence appears for spatially compact states. In lattice QCD, we find almost {it no} spatial boundary-condition dependence for the energy of the $cbar c$ system in $J/Psi$ and $eta_c$ channels for $Tsimeq(1.11-2.07)T_c$. We also investigate the spectral function of charmonia above $T_c$ in lattice QCD using the maximum entropy method (MEM) in terms of the boundary-condition dependence. There is {it no} spatial boundary-condition dependence for the low-lying peaks corresponding to $J/Psi$ and $eta_c$ around 3GeV at $1.62T_c$. These facts indicate the survival of $J/Psi$ and $eta_c$ as compact $cbar c$ (quasi-)bound states for $T_c < T < 2T_c$.
