J. Korean Math. Soc. 45 (2008), No. 3, pp. 645–681 EXISTENCE RESULT FOR HEAT-CONDUCTING VISCOUS INCOMPRESSIBLE FLUIDS WITH VACUUM Yonggeun Cho and Hyunseok Kim ∗ Reprinted from the Journal of the Korean Mathematical Society Vol. 45, No. 3, May 2008 c 2008 The Korean Mathematical Society