One-dimensional Compressible Navier-Stokes Equations with Temperature Dependent Transport Coefficients and Large Data

This paper is concerned with the Cauchy problem of the one-dimensional compressible Navier–Stokes equations with degenerate temperature dependent transport coefficients which satisfy conditions from the consideration in kinetic theory. A result on the existence and uniqueness of a globally smooth nonvacuum solution is obtained provided that the (γ − 1) · (H³(R)-norm of the initial perturbation)< C for some positive constant C independent of γ − 1. Here γ > 1 is the adiabatic gas constant. This is a Nishida–Smoller type global solvability result with large data.