Abstract
In this paper, we consider the initial boundary value problem for the one-dimensional Navier–Stokes equations for viscous compressible and heat-conducting fluids in a bounded domain with the Robin boundary condition on temperature. There are few results until now about global existence of regular solutions to the full Navier–Stokes equations with the Robin boundary condition on temperature. By the analysis of the effect of boundary dissipation, we derive the global existence of classical solution to the corresponding initial boundary value problem with large initial data and vacuum. This result could be viewed as the first one on the global well-posedness of classical solutions to the full Navier–Stokes equations in a bounded domain with the Robin boundary condition on temperature.
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