Global classical solution to a one-dimensional compressible non-Newtonian fluid with large initial data and vacuum

Because of the stronger nonlinearity and degeneracies of the density due to the momentum equation and appearance of vacuum, there are few results until now about global existence of classical solution to a compressible non-Newtonian fluid. In this paper, the global-in-time existence and uniqueness of classical solution to the initial-boundary-value problem is established for a one-dimensional compressible non-Newtonian fluid with large initial data and vacuum. Our analysis is based on some delicate energy estimates together with the iterate method being used ingeniously.