We study the possibility of a cool disk existing in the Galactic Center in the framework of the disk-corona evaporation/condensation model. Assuming an inactive disk near the gravitational capture distance left over from an earlier evolutionary stage, a hot corona should form above the disk since there is a continuous supply of hot gas from stellar winds of the close-by massive stars. We study the interaction between the disk and the corona. Whether the cool disk can survive depends on the mass exchange between disk and corona which is determined by the energy and pressure balance. If evaporation is the dominant process and the rate is larger than the Bondi accretion rate in the Galactic Center, the disk will be depleted within a certain time and no persistent disk will exist. On the other hand, if the interaction results in hot gas steadily condensing into the disk, an inactive cool disk with little gas accreting towards the central black hole might survive in the Galactic Center. For this case we further investigate the Bremsstrahlung radiation from the hot corona and compare it with the observed X-ray luminosity. Our model shows that, for standard viscosity in the corona ( alpha =0.3), the mass evaporation rate is much higher than the Bondi accretion rate and the coronal density is much larger than that inferred from Chandra observations. An inactive disk can not survive such strong evaporation. For small viscosity ( alpha < 0.07) we find condensation solutions. But detailed coronal structure computations show that in this case there is too much X-ray radiation from the corona to be in agreement with the observations. From this modeling we conclude that there should be no thin/inactive disk presently in the Galactic Center. However we do not exclude that the alternative non-radiative model of Nayakshin (2004) might instead be realized in nature and shortly discuss this question.