GLOBAL SMOOTH SOLUTIONS OF THE EQUATIONS OF A VISCOUS, HEAT-CONDUCTING, ONE-DIMENSIONAL GAS WITH DENSITY-DEPENDENT VISCOSITY

We consider initial boundary Value problems for the equations of the o ne-dimensional motion of a viscous, heat-conducting gas with density-d ependent viscosity that decreases (to zero) with decreasing density. W e prove that if the viscosity does not decrease to zero too rapidly, t hen smooth solutions exist globally in time.