  We numerically examine the influence of the viscosity on the relaxation
process of localized clouds in thermally unstable two-phase media, which are
locally heated by cosmic ray and cooled by radiation. Pulselike stationary
solutions of the media are numerically obtained by a shooting method. In
one-dimensional direct numerical simulations, localized clouds are formed
during the two-phase separation and sustained extraordinarily. Such long-lived
clouds have been recently observed in interstellar media. We demonstrate that
the balance of the viscosity with a pressure gradient remarkably suppresses the
evaporation of the clouds and controls the relaxation process. This balance
fixes the peak pressure of localized structures and then the structure is
attracted and trapped to one of the pulselike stationary solutions. While the
viscosity has been neglected in most of previous studies, our study suggests
that the precise treatment of the viscosity is necessary to discuss the
evaporation of the clouds.
