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 one-dimensional motion of a viscous, heat-conducting gas with density-dependent viscosity that decreases (to zero) with decreasing density. We prove that if the viscosity does not decrease to zero too rapidly, then smooth solutions exist globally in time.